INVESTOR RIGHTS AGREEMENT

Exhibit 4.10

Execution Version

INVESTOR RIGHTS AGREEMENT

This Investor Rights Agreement (this “Agreement”) is entered into as of December 1, 2006 by and between Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”), and Jefferies & Company, Inc., (the “Investor” and, individually or with any subsequent holders of Registrable Securities, a “Holder”).

WHEREAS, pursuant to the Purchase Agreement, dated November 28, 2006 (the “Purchase Agreement”), between the Company and the Investor, the Company has granted to the Investor a warrant (the “Warrants”) to purchase 110,000 shares of common stock, $0.0006 par value, of the Company (the “Common Stock”); and

WHEREAS, the Company has agreed to provide the registration rights set forth in this Agreement in connection with the Warrants;

NOW, THEREFORE, for and in consideration of the mutual covenants and conditions as set forth in the in the Purchase Agreement, the Warrants and this Agreement, the parties hereto hereby agree as follows:

(a) Demand Registration Rights. Upon the written request of Holders of a majority of the Registrable Securities, the Company will use commercially reasonable efforts to promptly file and cause to become effective in accordance with Section 2 a Registration Statement under the Securities Act on such form as is appropriate covering the offer and sale from time to time, by the methods of distribution designated by the Holders to the Company in writing, such number of Registrable Securities as it has received written requests from Holders to include within such Registration Statement, which shall include a duly completed selling stockholder questionnaire in the form provided by the Company. Notwithstanding the foregoing and notwithstanding any provision of this Agreement to the contrary, the Company shall not be obligated to file and cause to become effective more than one (1) Registration Statement pursuant to this Section 1(a).

(b) Piggyback Registration Rights. In the event the Company intends to file a Registration Statement under the Securities Act (other than on Form S-4 or Form S-8 or any successor form for the registration of securities issued or to be issued in connection with a merger or acquisition or employee benefit plan) covering the offer and sale of Common Stock by the Company or by other selling shareholders, the Company shall give written notice thereof to the Holders, and the Company shall include in such registration such number of Registrable Securities for which it has received written requests (which shall include a duly completed selling stockholder questionnaire in the form provided by the Company) from Holders to include within such Registration Statement within fifteen (15) days after the Company has sent written notice to such Holders.

(c) Underwritten Offerings. If the Registration Statement under subsection (b) above is to cover an Underwritten Offering, the Registrable Securities shall be included in the

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underwriting on the same terms and conditions as the securities otherwise being sold through the underwriters. If, in the good faith judgment of the managing underwriter in any Underwritten Offering, the inclusion of all of the shares of Registrable Securities and any other Common Stock requested to be registered in such Underwritten Offering would interfere with the successful marketing of a smaller number of such shares, then the number of shares of Registrable Securities and other Common Stock to be included in the offering (except for shares to be issued by the Company in an offering initiated by the Company) shall be reduced to such smaller number as the managing underwriter shall in its sole discretion determine. The reduction in participation by Holders of Registrable Securities shall occur on a pro rata basis with all other participating holders of securities to be registered under such Registration Statement, except to the extent that certain holders of other securities may have a contractual preference to participate granted prior to the date hereof. In such case, the Company and the managing underwriter shall use their reasonable best efforts to accommodate the selling desires of the Holders of Registrable Securities and the Holders of other shares of Common Stock of the Company who possess such registration rights. Any shares for which the Company has received written request to register and are excluded from an Underwritten Offering as discussed above, shall be withheld from the market by the holders thereof for a period of time, not to exceed 30 days prior to the effective date and 90 days thereafter, that the managing underwriter reasonably determines is necessary in order to effect the Underwritten Offering.

If and whenever the Company is required to register Registrable Securities, the Company will use its reasonable best efforts to effect such registration to permit the sale of such Registrable Securities in accordance with the Holders, intended plan of distribution thereof (as communicated in writing to the Company), and pursuant thereto the Company will as expeditiously as possible:

(a) (i) (A) prepare and file with the SEC as soon as practicable (and in any event, subject to the last paragraph of this Section 2, within 45 days after any written request made pursuant to Section 1(a)) a Form S-3 Registration Statement, or a Form S-1 Registration Statement if the Company is not then eligible to use Form S-3 (or in the last case the successor form), with respect to such Registrable Securities and use its reasonable best efforts to cause such Registration Statement to become effective as soon as possible and remain continuously effective and (B) prepare and file with the SEC such amendments and post-effective amendments to the Registration Statement, and such supplements to the related prospectus, as may be reasonably requested by the Holders or any underwriter of Registrable Securities or as may be required by the rules, regulations or instructions applicable to the registration form used by the Company or by the Securities Act or rules and regulations thereunder to keep the Registration Statement effective, in the case of either foregoing clause (A) or foregoing clause (B), until all of the Registrable Securities covered by such Registration Statement have been sold under the Registration Statement or cease to be Registrable Securities, (ii) include in such Registration Statement and/or Prospectus (as the case may be) the names of the Holders who have delivered written notice, and a duly completed selling stockholder questionnaire (in the form provided by the Company) to the Company at least five business days prior to the date that the Registration Statement is first declared effective, that they propose to include Registrable Securities in the Registration Statement as selling securityholders, and (iii) file pursuant to

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Rule 424(b) under the Securities Act a supplement to the prospectus contained in the registration Statement or, if required, file a post-effective amendment to the Registration Statement, in each case, to cover new Holders of Registrable Securities upon at least seven business days prior written notice by such new Holders to such effect and the delivery by such new Holders of duly completed selling stockholder questionnaires (in the form provided by the Company).

(b) [reserved]

(c) deliver to the Holders and the underwriters, if any, without charge, as many copies of each prospectus (and each preliminary prospectus) and any amendments or supplements thereto as such Persons may reasonably request (the Company hereby consenting to the use of each such prospectus (or preliminary prospectus) by the Holders and the underwriters, if any, in connection with the offering and sale of the Registrable Securities covered by such prospectus (or preliminary prospectus).

(d) register or qualify or cooperate with the Holders, the underwriters, if any, and their respective counsel in connection with the registration or qualification of such Registrable Securities for offer and sale under the securities or blue sky laws of such jurisdictions as the Holders or underwriters may designate in writing and do anything else necessary or advisable to enable the disposition in such jurisdictions of the Registrable Securities covered by the Registration Statement; provided 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 which would subject it to general service of process in any such jurisdiction where it is not then so subject.

(e) The Company shall give written notice to the Holders of the Registrable Securities included within the coverage of the Registration Statement (which notice pursuant to clauses (ii)-(v) hereof shall be accompanied by an instruction to suspend the use of the prospectus until the requisite changes have been made):

(i) when the Registration Statement or any amendment thereto has been filed with the SEC and when the Registration Statement or any post-effective amendment thereto has become effective;

(ii) of any request by the SEC for amendments or supplements to the Registration Statement or the prospectus included therein or for additional information;

(iii) of the issuance by the SEC of any stop order suspending the effectiveness of the Registration Statement or the initiation of any proceedings for that purpose;

(iv) of the receipt by the Company or its legal counsel of any notification with respect to the suspension of the qualification of the Securities for sale in any jurisdiction or the initiation or threatening of any proceeding for such purpose; and

(v) of the happening of any event that requires the Company to make changes in the Registration Statement or the prospectus in order that the Registration Statement or the prospectus do not contain an untrue statement of a material fact nor omit to state a material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading.

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(f) The Company shall make every reasonable effort to obtain the withdrawal, at the earliest possible time, of any order suspending the effectiveness of the Registration Statement.

(g) The Company shall furnish to each Holder of Registrable Securities included within the coverage of the Registration Statement, without charge, if the Holder so requests in writing, at least one copy of the Registration Statement and any post-effective amendment thereto, including, but only if expressly requested by such Holder, financial statements and schedules and all exhibits thereto (including those, if any, incorporated by reference).

(h) The Company shall cooperate with the Holders of the Registrable Securities to facilitate the timely preparation and delivery of certificates (if any) representing the Registrable Securities to be sold pursuant to the Registration Statement free of any restrictive legends and in such denominations and registered in such names as the Holders may request a reasonable period of time prior to sales of the Registrable Securities pursuant to the Registration Statement.

(i) Upon the occurrence of any event contemplated by paragraphs (ii) through (v) of Section 2(e) above, the Company shall promptly prepare and file a post-effective amendment to the Registration Statement or a supplement to the related prospectus and any other required document so that, as thereafter delivered to Holders of the Registrable Securities or purchasers of Registrable Securities, the prospectus will not contain an 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 light of the circumstances under which they were made, not misleading. If the Company notifies the Holders of Registrable Securities included within the coverage of the Registration Statement to suspend the use of the prospectus as a result of any of the events described in paragraphs (ii) through (v) of Section 2(e) above, until (A) the requisite changes to the prospectus have been made and the Holders have received copies of a supplemented or amended prospectus or (B) the Holders have been advised in writing by the Company that the use of the prospectus may be resumed, the Holders shall suspend use of such prospectus.

(j) The Company may require each Holder of Registrable Securities to be sold pursuant to the Registration Statement to furnish to the Company, pursuant to a questionnaire or otherwise, such information regarding the Holder and the distribution of the Registrable Securities as the Company may from time to time reasonably require for inclusion in the Registration Statement, and the Company may exclude from such registration the Registrable Securities of any Holder that fails to furnish such information within the applicable time period specified in this Agreement.

(k) In the case of any registration, the Company shall (i) make reasonably available for inspection by the Holders of the Registrable Securities, any underwriter participating in any disposition pursuant to the Registration Statement and any attorney, accountant or other agent retained by the Holders of the Registrable Securities or any such underwriter all relevant financial and other records, pertinent corporate documents and properties of the Company and (ii) cause the Company’s officers, directors, employees, accountants and auditors to supply all relevant information reasonably requested by the Holders of the Registrable Securities or any such underwriter, attorney, accountant or agent in connection with the Registration Statement, in each case, as shall be reasonably necessary to enable such persons, to conduct a reasonable investigation within the meaning of Section 11 of the Securities Act; provided, however, that the foregoing inspection and information gathering shall be coordinated on behalf of Holders by the Investor or by one counsel designated by the Holders.

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(l) In the case of any registration, the Company, if requested by any Holder of Registrable Securities covered thereby in connection with an underwritten offering of the Registrable Securities pursuant to the Registration Statement, shall cause (i) its counsel (which may include the Company’s general counsel and/or the Company’s outside counsel) to deliver an opinion or opinions and updates thereto relating to the Registrable Securities in customary form addressed to the underwriters thereof and dated, in the case of the initial opinion, the effective date of such Registration Statement (it being agreed that the matters to be covered by such opinion shall include, without limitation, the due incorporation and good standing of the Company and its subsidiaries; the qualification of the Company and its subsidiaries to transact business as foreign corporations; the due authorization, execution and delivery of the relevant underwriting agreement; the due authorization, execution, authentication and issuance, and the validity and enforceability, of the Registrable Securities; the absence of material legal or governmental proceedings involving the Company and its subsidiaries; the absence of governmental approvals required to be obtained in connection with the Registration Statement, the offering and sale of the Registrable Securities; the compliance as to form of such Registration Statement and any documents incorporated by reference therein with the requirements of the Securities Act and the Exchange Act; and, as of the date of the opinion and as of the effective date of the Registration Statement or most recent post-effective amendment thereto, as the case may be, the absence from such Registration Statement and the prospectus included therein, as then amended or supplemented, and from any documents incorporated by reference therein of an untrue statement of a material fact or the omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading (in the case of any such documents, in the light of the circumstances existing at the time that such documents were filed with the Commission under the Exchange Act); (ii) its officers to execute and deliver all customary documents and certificates and updates thereof requested by any underwriters of the Registrable Securities and (iii) its independent public accountants to provide to the underwriter(s) of the Registrable Securities a comfort letter in customary form and covering matters of the type customarily covered in comfort letters in connection with primary underwritten offerings, subject to receipt of appropriate documentation as contemplated, and only if permitted, by Statement of Auditing Standards No. 72.

(m) The Company shall use its reasonable best efforts to cause the Common Stock included in such Registration Statement to be, upon resale thereunder, listed on each U.S. securities exchange or national quotation system, if any, on which any shares of Common Stock are then listed.

Notwithstanding the undertakings in this Section 2, in the event the Board of Directors of the Company in good faith determines that significant corporate developments preclude the filing of a Registration Statement or its being declared effective, the Company may delay the filing or effectiveness of such Registration Statement for a period not to exceed 30 days from the date of such request, after giving notice to any Holder of Registrable Securities to be covered by such Registration Statement.

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The Registration Expenses in connection with all registrations shall be borne by the Company, except that (i) the fees and disbursements of any counsel to the Holders shall be paid by such Holders if such Holders are unwilling to be represented by counsel to the Company, and (ii) the Holders shall pay all underwriting discounts or commissions, any selling commissions and stock transfer taxes attributable to sales of their Registrable Securities. The Company will bear its internal expenses (including, without limitation, all salaries and expenses of its officers and employees performing legal or accounting duties), the expenses of any annual audit and the fees and expenses of any person, including special experts, retained by the Company.

(a) The Company agrees to indemnify and hold harmless the Holders and each person, if any, who controls any Holder within the meaning of the Securities Act or the Exchange Act and the respective officers, directors, partners, employees, representatives and agents of such Holder or any controlling p