WARRANT AGREEMENT

THESE SECURITIES AND THE SECURITIES ISSUABLE UPON THEIR EXERCISE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 AND MAY NOT BE TRANSFERRED UNLESS COVERED BY AN EFFECTIVE REGISTRATION STATEMENT UNDER SAID ACT, A "NO ACTION" LETTER FROM THE SECURITIES AND EXCHANGE COMMISSION WITH RESPECT TO SUCH TRANSFER, A TRANSFER MEETING THE REQUIREMENTS OF RULE 144 OF THE SECURITIES AND EXCHANGE COMMISSION, OR AN OPINION OF COUNSEL SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY SUCH TRANSFER IS EXEMPT FROM SUCH REGISTRATION.

Hyperdynamics Corp., Inc. , a corporation organized under the laws of the State of Delaware (the "Company"), hereby certifies that, for value received from Dutchess Private Equities Fund, II, L.P., ("Holder"), is entitled, subject to the terms set forth below, to purchase from the Company up to a total of five hundred thousand (500,000) shares of Common Stock, $.001 par value per share (the "Common Stock"), of the Company (each such share, a "Warrant Share" and all such shares, the "Warrant Shares") at an exercise price equal to the Fixed Conversion Price (as defined in the Debenture Agreement). The Warrant may be exercised on a cashless basis anytime after issuance through and including the fifth (5th) anniversary of its issuance (the "Expiration Date"), subject to the following terms and conditions:

1.   Registration of Warrant . The Company shall register this Warrant, upon records to be maintained by the Company for that purpose (the "Warrant Register"), in the name of the record Holder hereof from time to time. The Company may deem and treat the registered Holder of this Warrant as the absolute owner hereof for the purpose of any exercise hereof or any distribution to the Holder, and for all other purposes, and the Company shall not be affected by notice to the contrary.

2.   Registration of Transfers and Exchanges .

(a)   The Company or the transfer agent shall enter or record the transfer of any portion of this Warrant in the Warrant Register, upon surrender of this Warrant to the Transfer Agent or to the Company at the office specified in or pursuant to Section 3(b). Upon any such registration or transfer, a new warrant to purchase Common Stock, in substantially the form of this Warrant (any such new warrant, a "New Warrant"), evidencing the portion of this Warrant so transferred shall be issued to the transferee and a New Warrant evidencing the remaining portion of this Warrant not so transferred, if any, shall be issued to the transferring Holder. The acceptance of the New Warrant by the transferee thereof shall be deemed the acceptance of such transferee of all of the rights and obligations of a holder of a Warrant.

(b)   This Warrant is exchangeable, upon the surrender hereof by the Holder to the office of the Company specified in or pursuant to Section 3(b) for one or more New Warrants, evidencing in the aggregate the right to purchase the number of Warrant Shares which may then be purchased hereunder. Any such New Warrant will be dated the date of such exchange.

3.   Duration and Exercise of Warrants .

(a)   This Warrant shall be exercisable by the registered Holder on any business day before 5:00 P.M., Boston time, at any time and from time to time on or after the date hereof to and including the Expiration Date. At 5:00 P.M., Boston time on the Expiration Date, the portion of this Warrant not exercised prior thereto shall be and become void and of no value. Prior to the Expiration Date, the Company may not call or otherwise redeem this Warrant without the prior written consent of the Holder.

(b)   Subject to Sections 2(b), 6 and 10, upon surrender of this Warrant, with the Form of Election to Purchase attached hereto duly completed and signed, to the Company at its address for notice set forth in Section 12 and upon payment of the Exercise Price multiplied by the number of Warrant Shares that the Holder intends to purchase hereunder, in the manner provided hereunder, all as specified by the Holder in the Form of Election to Purchase, the Company shall promptly (but in no event later than 5 business days after the Date of Exercise (as defined herein)) issue or cause to be issued and cause to be delivered to or upon the written order of the Holder and in such name or names as the Holder may designate, a certificate for the Warrant Shares issuable upon such exercise, free of restrictive legends except (i) either in the event that a registration statement covering the resale of the Warrant Shares and naming the Holder as a selling stockholder thereunder is not then effective or the Warrant Shares are not freely transferable without volume restrictions pursuant to Rule 144(k) promulgated under the Securities Act of 1933, as amended (the "Securities Act"), or (ii) if this Warrant shall have been issued pursuant to a written agreement between the original Holder and the Company, as required by such agreement. Any person so designated by the Holder to receive Warrant Shares shall be deemed to have become holder of record of such Warrant Shares as of the Date of Exercise (as defined in this subsection) of this Warrant. A "Date of Exercise" means the date on which the Company shall have received (i) this Warrant (or any New Warrant, as applicable), with the Form of Election to Purchase attached hereto (or attached to such New Warrant) appropriately completed and duly signed, and (ii) payment of the Exercise Price for the number of Warrant Shares so indicated by the holder hereof to be purchased.

(c)   This Warrant shall be exercisable, either in its entirety or, from time to time, for a portion of the number of Warrant Shares. If less than all of the Warrant Shares which may be purchased under this Warrant are exercised at any time, the Company shall issue or cause to be issued, at its expense, a New Warrant evidencing the right to purchase the remaining number of Warrant Shares for which no exercise has been evidenced by this Warrant. In the event the Common Stock representing the Warrant Shares is not delivered per the written instructions of the Purchaser, within ten (10) business days after the Notice of Election and Warrant is received by the Company (the “Delivery Date”), then in such event the Company shall pay to Holder one-half percent (0.5%) in cash, of the dollar value of the Warrant Shares to be issued per each day after the Delivery Date that the Warrant Shares are not delivered. The Company acknowledges that its failure to deliver the Warrant Shares by the Delivery Date will cause the Holder to suffer damages in an amount that will be difficult to ascertain. Accordingly, the parties agree that it is appropriate to include in this Warrant a provision for liquidated damages. The parties acknowledge and agree that the liquidated damages provision set forth in this section represents the parties’ good faith effort to quantify such damages and, as such, agree that the form and amount of such liquidated damages are reasonable and will not constitute a penalty. The payment of liquidated damages shall not relieve the Company from its obligations to deliver the Common Stock pursuant to the terms of this Warrant. The Company shall make any payments incurred under this Section 3 in immediately available funds within ten (10) business days from the date of issuance of the applicable Warrant Shares. Nothing herein shall limit Holder’s right to pursue actual damages or cancel the Notice of Election for the Company’s failure to issue and deliver Common Stock to the Holder within fifteen (15) business days following the Delivery Date.

4.   Registration Rights . During the term of this Warrant, the Company agrees to use its best efforts to file, within fifteen (15) days of the Company filing its Form 10K for 2005, but in no event later than October 15, 2005, a registration statement with the Securities and Exchange Commission covering the resale of the Warrant Shares and naming the Holder as a selling stockholder thereunder (unless the Warrant Shares are otherwise freely transferable without volume restrictions pursuant to Rule 144(k) or Rule 144A promulgated under the Act). The registration rights granted to the Holder pursuant to this Section shall continue until all of the Holder's Warrant Shares have been sold in accordance with an effective registration statement or upon the Expiration Date. The Company will pay all registration expenses in connection therewith.

5. Payment of Taxes . The Company will pay all documentary stamp taxes attributable to the issuance of Warrant Shares upon the exercise of this Warrant; provided, however, that the Company shall not be required to pay any tax that may be payable in respect of any transfer involved in the registration of any certificates for Warrant Shares or Warrants in a name other than that of the Holder. The Holder shall be responsible for all other tax liability that may arise as a result of holding or transferring this Warrant or receiving Warrant Shares upon exercise hereof.

6.   Replacement of Warrant . If this Warrant is mutilated, lost, stolen or destroyed, the Company shall issue or cause to be issued in exchange and substitution for and upon cancellation hereof, or in lieu of and substitution for this Warrant, a New Warrant, but only upon receipt of evidence reasonably satisfactory to the Company of such loss, theft or destruction and indemnity, if requested, satisfactory to it. Applicants for a New Warrant under such circumstances shall also comply with such other reasonable regulations and procedures and pay such other reasonable charges as the Company may prescribe.

7.   Reservation of Warrant Shares . The Company covenants that it will at all times reserve and keep available out of the aggregate of its authorized but unissued Common Stock, solely for the purpose of enabling it to issue Warrant Shares upon exercise of this Warrant as herein provided, the number of Warrant Shares which are then issuable and deliverable upon the exercise of this entire Warrant, free from preemptive rights or any other actual contingent purchase rights of persons other than the Holder (taking into account the adjustments and restrictions of Section 8. The Company covenants that all Warrant Shares that shall be so issuable and deliverable shall, upon issuance and the payment of the applicable Exercise Price in accordance with the terms hereof, be duly and validly authorized, issued and fully paid and nonassessable. If the Company does not have a sufficient amount of Common Stock authorized to reserve for the Warrant Shares, it shall use its best efforts to place before shareholder vote a proposal to increase the number of its authorized shares as soon as reasonably practicable.

8.   Certain Adjustments . The Exercise Price and number of Warrant Shares issuable upon exercise of this Warrant are subject to adjustment from time to time as set forth in this Section 8. Upon each such adjustment of the Exercise Price pursuant to this Section 8, the Holder shall thereafter prior to the Expiration Date be entitled to purchase, at the Exercise Price resulting from such adjustment, the number of Warrant Shares obtained by multiplying the Exercise Price in effect immediately prior to such adjustment by the number of Warrant Shares issuable upon exercise of this Warrant immediately prior to such adjustment and dividing the product thereof by the Exercise Price resulting from such adjustment.

(a)   If the Company, at any time while this Warrant is outstanding, (i) shall pay a stock dividend (except scheduled dividends paid on outstanding preferred stock as of the date hereof which contain a stated dividend rate) or otherwise make a distribution or distributions on shares of its Common Stock or on any other class of capital stock and not the Common Stock payable in shares of Common Stock, (ii) subdivide outstanding shares of Common Stock into a larger number of shares, or (iii) combine outstanding shares of Common Stock into a smaller number of shares, the Exercise Price shall b