INVESTOR RIGHTS AGREEMENT

Exhibit 10.2

INVESTOR RIGHTS AGREEMENT

This Investor Rights Agreement (this “Agreement”) is made and entered into as of August 30, 2005 among Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”), and each of the purchasers executing this Agreement and listed on Schedule 1 attached hereto (collectively, the “Purchasers”).

This Agreement is being entered into pursuant to the Convertible Promissory Note and Warrant Purchase Agreement, dated as of [the date hereof,] by and among the Company and the Purchasers (the “Purchase Agreement”).

The Company and the Purchasers hereby agree as follows:

Capitalized terms used and not otherwise defined herein shall have the meanings given such terms in the Purchase Agreement. As used in this Agreement, the following terms shall have the following meanings:

“ Advice ” shall have the meaning set forth in Section 3(m).

“ Affiliate ” means, with respect to any Person, any other Person that directly or indirectly controls or is controlled by or under common control with such Person. For the purposes of this definition, “control,” when used with respect to any Person, means the possession, direct or indirect, of the power to direct or cause the direction of the management and policies of such Person, whether through the ownership of voting securities, by contract or otherwise; and the terms “affiliated,” “controlling” and “controlled” have meanings correlative to the foregoing.

“ Blackout Period ” shall have the meaning set forth in Section 3(n).

“ Board ” shall have the meaning set forth in Section 3(n).

“ Business Day ” means any day except Saturday, Sunday and any day which shall be a legal holiday or a day on which banking institutions in the State of Texas generally are authorized or required by law or other government actions to close.

“ Closing Date ” means the Closing Date as defined in the Purchase Agreement.

“ Commission ” means the Securities and Exchange Commission.

“ Common Stock ” means the Company’s Common Stock, par value $0.0006 per share.

“ Demand Notice ” has the meaning set forth in Section 2(a).

“ Effectiveness Period ” means the period after a Registration Statement becomes effective until such date as is the earlier of (x) the date when all Registrable Securities

covered by such Registration Statement have been sold or (y) the date on which the Registrable Securities may be sold without any restriction pursuant to Rule 144(k) as determined by the counsel to the Company pursuant to a written opinion letter, addressed to the Company’s transfer agent to such effect.

“ Event ” shall have the meaning set forth in Section 8(e).

“ Exchange Act ” means the Securities Exchange Act of 1934, as amended.

“ Filing Date ” means the 45th day following the date of receipt by the Company of a Demand Notice, or in the case of a Registration Statement pursuant to Section 8(d) the 45 ^th day following receipt by the Holder of written notice of the Company’s determination to proceed with such a Registration Statement.

“ Holder ” or “ Holders ” means the holder or holders, as the case may be, from time to time of Registrable Securities, including without limitation the Purchasers and their assignees.

“ Indemnified Party ” shall have the meaning set forth in Section 5(c).

“ Indemnifying Party ” shall have the meaning set forth in Section 5(c).

“ Initiating Holders ” has the meaning set forth in Section 2(a).

“ Losses ” shall have the meaning set forth in Section 5(a).

“ Notes ” means the Convertible Promissory Notes issued pursuant to the Purchase Agreement.

“ Person ” means an individual or a corporation, partnership, trust, incorporated or unincorporated association, joint venture, limited liability company, joint stock company, government (or an agency or political subdivision thereof) or other entity of any kind.

“ Proceeding ” means an action, claim, suit, investigation or proceeding (including, without limitation, an investigation or partial proceeding, such as a deposition), whether commenced or threatened.

“ Prospectus ” means the prospectus included in any Registration Statement (including, without limitation, a prospectus that includes any information previously omitted from a prospectus filed as part of an effective registration statement in reliance upon Rule 430A promulgated under the Securities Act), as amended or supplemented by any prospectus supplement, with respect to the terms of the offering of any portion of the Registrable Securities covered by such Registration Statement, and all other amendments and supplements to the Prospectus, including post-effective amendments, and all material incorporated by reference in such Prospectus.

“ Registrable Securities ” means (a) the Warrant Shares (without regard to any limitations on beneficial ownership contained therein) or other securities issued or issuable

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to each Purchaser or its transferee or designee (i) upon exercise of the Warrants, or (ii) upon any dividend or distribution with respect to, any exchange for or any replacement of such Warrants or (iii) upon any conversion, exercise or exchange of any securities issued in connection with any such distribution, exchange or replacement; (b) securities issued or issuable upon any stock split, stock dividend, recapitalization or similar event with respect to the foregoing; and (c) any other security issued as a dividend or other distribution with respect to, in exchange for, in replacement or redemption of, or in reduction of the liquidation value of, any of the securities referred to in the preceding clauses; provided, however, that such securities shall cease to be Registrable Securities when such securities have been sold to or through a broker or dealer or underwriter in a public distribution or a public securities transaction or when such securities may be sold without any restriction pursuant to Rule 144(k) as determined by the counsel to the Company pursuant to a written opinion letter, addressed to the Company’s transfer agent to such effect as described in Section 2 of this Agreement.

“ Registration Statement ” means the registration statements and any additional registration statements contemplated by Section 2 and Section 8(d), including (in each case) the Prospectus, amendments and supplements to such registration statement or Prospectus, including pre- and post-effective amendments, all exhibits thereto, and all material incorporated by reference in such registration statement.

“ Rule 144 ” means Rule 144 promulgated by the Commission pursuant to the Securities Act, as such Rule may be amended from time to time, or any similar rule or regulation hereafter adopted by the Commission having substantially the same effect as such Rule.

“ Rule 158 ” means Rule 158 promulgated by the Commission pursuant to the Securities Act, as such Rule may be amended from time to time, or any similar rule or regulation hereafter adopted by the Commission having substantially the same effect as such Rule.

“ Securities Act ” means the Securities Act of 1933, as amended.

“ Special Counsel ” means Wiggin and Dana LLP.

“ Warrant Shares ” means the shares of Common Stock issuable upon the exercise of the warrants issued or to be issued to the Purchasers or their assignees or designees in connection with the offering consummated under the Purchase Agreement.

(a) At any time on or after the date that is the earlier of (i) three months after the Closing Date or (ii) the date on which the Notes are converted into New Securities (as defined in the Purchase Agreement), a Holder or Holders holding in the aggregate at least 50% of the Registrable Securities then outstanding (the “Initiating Holders”) may request, in writing (a “Demand Notice”), that the Company effect the registration on Form S-3 (or if such form is not available to the Company on another form appropriate for such registration in accordance herewith) of any Registrable Securities owned by such Initiating Holders.

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(b) Upon receipt of any request for registration pursuant to this Section 2, the Company shall promptly give written notice of such proposed registration to all other Holders. Such Holders shall have the right, by giving written notice to the Company within ten (10) days after the Company provides its notice, to elect to have included in such registration such of their Registrable Securities as such Holders may request in such notice of election, subject in the case of an underwritten offering to the terms of Section 2(c). Thereupon, the Company shall, as expeditiously as possible, use its best efforts to effect the registration of all Registrable Securities which the Company has been requested to so register (including filing with the Commission a request for acceleration of effectiveness in accordance with Rule 461 promulgated under the Securities Act within five (5) Business Days of the date that the Company is notified (orally or in writing, whichever is earlier) by the Commission that a Registration Statement will not be “reviewed,” or not be subject to further review) and to keep such Registration Statement continuously effective under the Securities Act during the Effectiveness Period. Such Registration Statement also shall cover, to the extent allowable under the Securities Act and the Rules promulgated thereunder (including Securities Act Rule 416), such indeterminate number of additional shares of Common Stock resulting from stock splits, stock dividends or similar transactions with respect to the Registrable Securities.

(c) If the Initiating Holders intend to distribute the Registrable Securities covered by their request by means of an underwriting, they shall so advise the Company as a part of their request made pursuant to Section 2(a) and the Company shall include such information in its written notice referred to in Section 2(b). In such event, (i) the right of any other Holder to include its Registrable Securities in such registration pursuant to Section 2(a) shall be conditioned upon such other Holder’s participation in such underwriting on the terms set forth herein, and (ii) all Holders including Registrable Securities in such registration shall enter into an underwriting agreement upon customary terms with the underwriter or underwriters managing the offering. The Initiating Holders shall have the right to select the managing underwriter(s) for any underwritten offering requested pursuant to Section 2(a) subject to the approval of the Company, which approval will not be unreasonably withheld, conditioned or delayed. If any Holder who has requested inclusion of its Registrable Securities in such registration as provided above disapproves of the terms of the underwriting, such person may elect, by written notice to the Company, to withdraw its Registrable Securities from such Registration Statement and underwriting. If the managing underwriter advises the Company in writing that marketing factors require a limitation on the number of shares to be underwritten, the number of Registrable Securities to be included in the Registration Statement and underwriting shall be allocated among all Holders requesting registration in proportion, as nearly as practicable, to the respective number of Registrable Securities held by them on the date of the request for registration made by the Initiating Holders pursuant to Section 2(a). If any Holder would thus be entitled to include more Registrable Securities than such Holder requested to be registered, the excess shall be allocated among other requesting Holders pro rata in the manner described in the preceding sentence.

(d) The Company shall not be required to effect more than one registration pursuant to Section 2(a). For purposes of this Section 2(d), a Registration Statement shall not be counted until such time as such Registration Statement has been declared effective by

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the Commission. For purposes of this Section 2(d), a Registration Statement shall not be counted if, as a result of an exercise of the underwriters’ cut-back provisions as set forth in Section 2(c), less than 50% of the total number of Registrable Securities that Holders have requested to be included in such Registration Statement are so included.

In connection with the Company’s registration obligations hereunder, the Company shall:

(a) Prepare and file with the Commission on or prior to the Filing Date, a Registration Statement on Form S-3 (or if such form is not available to the Company on another form appropriate for such registration in accordance herewith) (which shall include a Plan of Distribution substantially in the form of Exhibit A attached hereto), and cause the Registration Statement to become effective and remain effective as provided herein; provided, however, that not less than three (3) Business Days prior to the filing of the Registration Statement or any related Prospectus or any amendment or supplement thereto, the Company shall (i) furnish to the Special Counsel, copies of all such documents proposed to be filed, which documents (other than those incorporated by reference) will be subject to the review of such Special Counsel, and (ii) at the request of any Holder cause its officers and directors, counsel or independent certified public accountants, as applicable, to respond to such inquiries as shall be necessary, in the reasonable opinion of counsel to such Holders, to conduct a reasonable investigation within the meaning of the Securities Act. The Company shall not file the Registration Statement or any such Prospectus or any amendments or supplements thereto to which the Holders of a majority of the Registrable Securities or the Special Counsel shall reasonably object within three (3) Business Days after the Special Counsel’s receipt thereof.

(b) (i) Prepare and file with the Commission such amendments, including post-effective amendments, to the Registration Statement as may be necessary to keep the Registration Statement continuously effective as to the applicable Registrable Securities for the Effectiveness Period and to the extent any Registrable Securities are not included in such Registration Statement for reasons other than the failure of the Holder to comply with Section 3(m) hereof, shall prepare and file with the Commission such additional Registration Statements in order to register for resale under the Securities Act all Registrable Securities; (ii) cause the related Prospectus to be amended or supplemented by any required Prospectus supplement, and as so supplemented or amended to be filed pursuant to Rule 424 (or any similar provisions then in force) promulgated under the Securities Act; (iii) respond as promptly as possible, and in no event later than ten (10) Business Days, to any comments received from the Commission with respect to the Registration Statement or any amendment thereto and as promptly as possible provide the Holders true and complete copies of all correspondence from and to the Commission relating to the Registration Statement; and (iv) comply in all material respects with the provisions of the Securities Act and the Exchange Act with respect to the disposition of all Registrable Securities covered by the Registration Statement during the Effectiveness Period in accordance with the intended methods of disposition by the Holders thereof set forth in the Registration Statement as so amended or in such Prospectus as so supplemented.

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(c) Notify the Holders of Registrable Securities to be sold and the Special Counsel as promptly as possible (A) when a Prospectus or any Prospectus supplement or post-effective amendment to the Registration Statement is proposed to be filed (but in no event in the case of this subparagraph (A), less than three (3) Business Days prior to date of such filing); (B) when the Commission notifies the Company whether there will be a “review” of such Registration Statement and whenever the Commission comments in writing on such Registration Statement; and (C) with respect to the Registration Statement or any post-effective amendment, when the same has become effective, and after the effectiveness thereof: (i) of any request by the Commission or any other Federal or state governmental authority for amendments or supplements to the Registration Statement or Prospectus or for additional information; (ii) of the issuance by the Commission of any stop order suspending the effectiveness of the Registration Statement covering any or all of the Registrable Securities or the initiation of any Proceedings for that purpose; (iii) if at any time any of the representations and warranties of the Company contained in any agreement contemplated hereby ceases to be true and correct in all material respects; (iv) of the receipt by the Company of any notification with respect to the suspension of the qualification or exemption from qualification of any of the Registrable Securities for sale in any jurisdiction, or the initiation or threatening of any Proceeding for such purpose; and (v) if the financial statements included in the Registration Statement become ineligible for inclusion therein or of the occurrence of any event that makes any statement made in the Registration Statement or Prospectus or any document incorporated or deemed to be incorporated therein by reference untrue in any material respect or that requires any revisions to the Registration Statement, Prospectus or other documents so that, in the case of the Registration Statement or the Prospectus, as the case may be, it will not contain any untrue statement of a material fact or omit to state any material fact required to be stated therein or necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading.

(d) Use its best efforts to avoid the issuance of, or, if issued, use best efforts to obtain the withdrawal of, (i) any order suspending the effectiveness of the Registration Statement or (ii) any suspension of the qualification (or exemption from qualification) of any of the Registrable Securities for sale in any jurisdiction, at the earliest practicable moment.

(e) If reasonably requested by the Holders of a majority in interest of the Registrable Securities, (i) promptly incorporate in a Prospectus supplement or post-effective amendment to the Registration Statement such information as the Company reasonably agrees should be included therein and (ii) make all required filings of such Prospectus supplement or such post-effective amendment as soon as practicable after the Company has received notification of the matters to be incorporated in such Prospectus supplement or post-effective amendment; provided, however, that the Company shall not be required to take any action pursuant to this Section 3(e) that would, in the written opinion of counsel for the Company (addressed to the Special Counsel), violate applicable law.

(f) Furnish to each Holder and the Special Counsel, without charge, at least one conformed copy of each Registration Statement and each amendment thereto, including financial statements and schedules, and all exhibits to the extent requested by such Person (including those previously furnished or incorporated by reference) promptly after the filing of such documents with the Commission.

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(g) Promptly deliver to each Holder and the Special Counsel, without charge, as many copies of the Prospectus or Prospectuses (including each form of prospectus) and each amendment or supplement thereto as such Persons may reasonably request; and the Company hereby consents to the use of such Prospectus and each amendment or supplement thereto by each of the selling Holders in connection with the offering and sale of the Registrable Securities covered by such Prospectus and any amendment or supplement thereto.

(h) Prior to any public offering of Registrable Securities, use its reasonable commercial efforts to register or qualify or cooperate with the selling Holders and the Special Counsel in connection with the registration or qualification (or exemption from such registration or qualification) of such Registrable Securities for offer and sale under the securities or Blue Sky laws of such jurisdictions within the United States as any Holder requests in writing, to keep each such registration or qualification (or exemption therefrom) effective during the Effectiveness Period and to do any and all other acts or things necessary or advisable to enable the disposition in such jurisdictions of the Registrable Securities covered by a Registration Statement; provided, however, that the Company shall not be required to qualify generally to do business in any jurisdiction where it is not then so qualified or to take any action that would subject it to general service of process in any jurisdiction where it is not then so subject or subject the Company to any material tax in any such jurisdiction where it is not then so subject.

(i) Cooperate with the Holders to facilitate the timely preparation and delivery of certificates representing Registrable Securities to be sold pursuant to a Registration Statement, which certificates shall be free, to the extent permitted by applicable law and the Purchase Agreement, of all restrictive legends, and to enable such Registrable Securities to be in such denominations and registered in such names as any Holder may request at least two (2) Business Days prior to any sale of Registrable Securities. In connection therewith, the Company shall promptly after the effectiveness of the Registration Statement cause an opinion of counsel to be delivered to and maintained with its transfer agent, together with any other authorizations, certificates and directions required by the transfer agent, which authorize and direct the transfer agent to issue such Registrable Securities without legend upon sale by the Holder of such shares of Registrable Securities under the Registration Statement.

(j) Upon the occurrence of any event contemplated by Section 3(c)(C)(v), as promptly as possible, prepare a supplement or amendment, including a post-effective amendment, to the Registration Statement or a supplement to the related Prospectus or any document incorporated or deemed to be incorporated therein by reference, and file any other required document so that, as thereafter delivered, neither the Registration Statement nor such Prospectus will contain an untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading.

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(k) Cause all Registrable Securities relating to such Registration Statement to be listed on any United States securities exchange, quotation system, market or over-the-counter bulletin board, if any, on which similar securities issued by the Company are then listed as and when required pursuant to the Purchase Agreement.

(l) Comply in all material respects with all applicable rules and regulations of the Commission and make generally available to its security holders earning statements satisfying the provisions of Section 11(a) of the Securities Act and Rule 158 not later than 45 days after the end of any 3-month period (or 90 days after the end of any 12-month period if such period is a fiscal year) commencing on the first day of the first fiscal quarter of the Company after the effective date of the Registration Statement, which statement shall conform to the requirements of Rule 158.

(m) Request each selling Holder to furnish to the Company information regarding such Holder and the distribution of such Registrable Securities as is required by law or the Commission to be disclosed in the Registration Statement, and the Company may exclude from such registration the Registrable Securities of any such Holder who fails to furnish such information within a reasonable time prior to the filing of each Registration Statement, supplemented Prospectus and/or amended Registration Statement.

If the Registration Statement refers to any Holder by name or otherwise as the holder of any securities of the Company, then such Holder shall have the right to require (if such reference to such Holder by name or otherwise is not required by the Securities Act or any similar federal statute then in force) the deletion of the reference to such Holder in any amendment or supplement to the Registration Statement filed or prepared subsequent to the time that such reference ceases to be required.

Each Holder agrees by its acquisition of such Registrable Securities that, upon receipt of a notice from the Company of the occurrence of any event of the kind described in Section 3(c)(C)(i), 3(c)(C)(ii), 3(c)(C)(iii), 3(c)(C)(iv), 3(c)(C)(v) or 3(n), such Holder will forthwith discontinue disposition of such Registrable Securities under the Registration Statement until such Holder’s receipt of the copies of the supplemented Prospectus and/or amended Registration Statement contemplated by Section 3(j), or until it is advised in writing (the “Advice”) by the Company that the use of the applicable Prospectus may be resumed, and, in either case, has received copies of any additional or supplemental filings that are incorporated or deemed to be incorporated by reference in such Prospectus or Registration Statement.

(n) If (i) there is material non-public information regarding the Company which the Company’s Board of Directors (the “Board”) reasonably determines not to be in the Company’s best interest to disclose and which the Company is not otherwise required to disclose, or (ii) there is a significant business opportunity (including, but not limited to, the acquisition or disposition of assets (other than in the ordinary course of business) or any merger, consolidation, tender offer or other similar transaction) available to the Company which the Board reasonably determines not to be in the Company’s best interest to disclose and which the Company would be required to disclose under the Registration Statement, then the Company may postpone or suspend filing or effectiveness of a registration statement for a period not to exceed 30 consecutive days, provided that the Company may

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not postpone or suspend its obligation under this Section 3(n) for more than 45 days in the aggregate during any 12 month period (each, a “Blackout Period”). The payment requirements set forth in Sections 8(e) and (f) shall be tolled during and shall not be applicable with respect to any Blackout Period.

All fees and expenses incident to the performance of or compliance with this Agreement by the Company shall be borne by the Company whether or not the Registration Statement is filed or becomes effective and whether or not any Registrable Securities are sold pursuant to the Registration Statement. The fees and expenses referred to in the foregoing sentence shall include, without limitation, (i) all registration and filing fees (including, without limitation, fees and expenses (A) with respect to filings required to be made with each securities exchange, quotation system, market or over-the-counter bulletin board on which Registrable Securities are required hereunder to be listed, (B) with respect to filings required to be made with the Commission, and (C) in compliance with state or provincial securities or Blue Sky laws (including, without limitation, fees and disbursements of Special Counsel in connection with Blue Sky qualifications of the Registrable Securities and determination of the eligibility of the Registrable Securities for investment under the laws of such jurisdictions as the Holders of a majority of Registrable Securities may designate)), (ii) printing expenses (including, without limitation, expenses of printing certificates for Registrable Securities and of printing or photocopying prospectuses), (iii) messenger, telephone and delivery expenses, (iv) Securities Act liability insurance, if the Company desires such insurance, (v) fees and expenses of all other Persons retained by the Company in connection with the consummation of the transactions contemplated by this Agreement, including, without limitation, the Company’s independent public accountants (including, in the case of an underwritten offering, the expenses of any comfort letters or costs associated with the delivery by independent public accountants of a comfort letter or comfort letters) and legal counsel, and (vi) fees and expenses of the Special Counsel in connection with any Registration Statement hereunder. In addition, the Company shall be responsible for all of its internal expenses incurred in connection with the consummation of the transactions contemplated by this Agreement (including, without limitation, all salaries and expenses of its officers and employees performing legal or accounting duties), the expense of any annual audit and the fees and expenses incurred in connection with the listing of the Registrable Securities on any securities exchange as required hereunder. Notwithstanding the foregoing, the Holders shall pay all underwriting discounts or commissions, selling commissions and stock transfer taxes attributable to any sale of Registrable Securities.

(a) Indemnification by the Company . The Company shall, notwithstanding any termination of this Agreement, indemnify and hold harmless each Holder, the officers, directors, partners, agents, brokers (including brokers who offer and sell Registrable Securities as principal as a result of a pledge or any failure to perform under a margin call of Common Stock), investment advisors and employees of each of them, each Person who controls any such Holder (within the meaning of Section 15 of the Securities Act or Section

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20 of the Exchange Act) and the officers, directors, agents and employees of each such controlling Person, to the fullest extent permitted by applicable law, from and against any and all losses, claims, damages, liabilities, costs (including, without limitation, costs of preparation and reasonable attorneys’ fees) and expenses (collectively, “Losses”), as incurred, arising out of or relating to any untrue or alleged untrue statement of a material fact contained or incorporated by reference in the Registration Statement, any Prospectus or any form of prospectus or in any amendment or supplement thereto or in any preliminary prospectus, or arising out of or relating to any omission or alleged omission of a material fact required to be stated therein or necessary to make the statements therein (in the case of any Prospectus or form of prospectus or amendment or supplement thereto, in the light of the circumstances under which they were made) not misleading, except to the extent, but only to the extent, that (i) such untrue statements or omissions are based solely upon information regarding such Holder furnished in writing to the Company by such Holder expressly for use therein, which information was reasonably relied on by the Company for use therein or to th