COMMON STOCK PURCHASE WARRANT To Purchase 550,000 Shares of Common Stock of TRANSMERIDIAN EXPLORATION INCORPORATED

Exhibit 4.4

Execution Version

THIS WARRANT AND THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE OFFERED, SOLD, ASSIGNED OR TRANSFERRED, IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER SAID ACT OR UNLESS THE COMPANY HAS RECEIVED AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE COMPANY THAT REGISTRATION UNDER SAID ACT IS NOT REQUIRED.

Warrant No. J-102

COMMON STOCK PURCHASE WARRANT

To Purchase 550,000 Shares of Common Stock of

TRANSMERIDIAN EXPLORATION INCORPORATED

THIS IS TO CERTIFY THAT Jefferies & Company, Inc., or registered assigns (the “Holder”), is entitled, during the Exercise Period (as hereinafter defined), to purchase from Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”), the Warrant Stock (as hereinafter defined and subject to adjustment as provided herein), in whole or in part, at the Current Warrant Price (as hereinafter defined), all on and subject to the terms and conditions hereinafter set forth.

1. Definitions. As used in this Warrant, the following terms have the respective meanings set forth below:

“Affiliate” means any person or entity that, directly or indirectly through one or more intermediaries, controls or is controlled by or is under common control with a person or entity, as such terms are used in and construed under Rule 144 under the Securities Act. With respect to a Holder, any investment fund or managed account that is managed on a discretionary basis by the same investment manager as such Holder will be deemed to be an Affiliate of such Holder.

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

“Cashless Exercise” has the meaning set forth in Section 2.1(b).

“Change of Control” means the (i) acquisition by an individual or legal entity or group (as set forth in Section 13(d) of the Exchange Act) of more than one-half of the voting rights or equity interests in the Company; or (ii) sale, conveyance, or other disposition of all or substantially all of the assets, property or business of the Company or the merger into or consolidation with any other entity (other than a wholly owned subsidiary corporation) or effectuation of any transaction or series of related transactions where holders of the Company’s voting securities prior to such transaction or series of transactions fail to continue to hold at least 50% of the voting power of the Company.

“Closing Date” means June 18, 2007.

“Commission” means the Securities and Exchange Commission or any other federal agency then administering the Securities Act and other federal securities laws.

“Common Stock” means (except where the context otherwise indicates) the Common Stock, $0.0006 par value per share, of the Company as constituted on the Closing Date, and any capital stock into which such Common Stock may thereafter be changed or converted, and shall also include (i) capital stock of the Company of any other class (regardless of how denominated) issued to the holders of shares of Common Stock upon any reclassification thereof which is also not preferred as to dividends or assets on liquidation over any other class of stock of the Company and which is not subject to redemption and (ii) shares of common stock of any successor or acquiring corporation received by or distributed to the holders of Common Stock of the Company in the circumstances contemplated by Section 4.4.

“Common Stock Equivalents” means any stock or security convertible into or exchangeable for Common Stock and any right, warrants or option to acquire Common Stock or any such convertible or exchangeable security.

“Current Warrant Price” means, in respect of a share of Common Stock at any date herein specified, the price at which a share of Common Stock may be purchased pursuant to this Warrant on such date. Until the Current Warrant Price is adjusted pursuant to the terms hereof, the Current Warrant Price shall be equal to the Original Market Price.

“Exchange Act” means the Securities Exchange Act of 1934, as amended, or any similar federal statute, and the rules and regulations of the Commission thereunder, all as the same shall be in effect from time to time.

“Exercise Period” means the period during which this Warrant is exercisable pursuant to Section 2.1.

“Expiration Date” means June 18, 2014.

“GAAP” means generally accepted accounting principles in the United States of America as from time to time in effect.

“Market Price” means, as of any date of determination, the closing sale price per share (or if no closing sale price is reported, the average of the closing bid and ask prices or, if more than one in either case, the average of the average closing bid and the average closing ask prices) on such date as reported on the principal United States securities exchange on which the Warrant Stock is then traded or, if the Warrant Stock is not listed on a United States national or regional securities exchange, as reported by Nasdaq or by the Pink Sheets LLC, or if the Warrant Stock is not publicly traded, then as determined in good faith by the Company’s Board of Directors upon review of relevant factors.

“NASD” means the National Association of Securities Dealers, Inc., or any successor corporation thereto.

“Original Market Price” means, in respect of any share of Common Stock, $2.25 per share.

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“Other Property” has the meaning set forth in Section 4.4.

“Person” means any individual, sole proprietorship, partnership, joint venture, trust, incorporated organization, association, corporation, limited liability company, institution, public benefit corporation, entity or government (whether federal, state, county, city, municipal or otherwise, including, without limitation, any instrumentality, division, agency, body or department thereof).

“Restricted Common Stock” means shares of Common Stock which are, or which upon their issuance upon the exercise of any Warrant would be required to be, evidenced by a certificate bearing the restrictive legend set forth in Section 3.2.

“Securities Act” means the Securities Act of 1933, as amended, or any similar federal statute, and the rules and regulations of the Commission thereunder, all as the same shall be in effect at the time.

“Time of Sale” means June 18, 2007, at which time Jefferies & Company, Inc., acting as placement agent, completed the initial closing with respect to a private placement of an aggregate 550,000 shares of the Company’s 20% Junior Redeemable Convertible Preferred Stock.

“Trading Day” means any day on which the primary market on which shares of Common Stock are listed is open for trading.

“Transfer” means any disposition of any Warrant or Warrant Stock or of any interest in either thereof, which would constitute a sale thereof within the meaning of the Securities Act.

“Warrant Price” means an amount equal to (i) the number of shares of Common Stock being purchased upon exercise of this Warrant pursuant to Section 2.1, multiplied by (ii) the Current Warrant Price.

“Warrant Stock” means any of the shares of Common Stock issued upon the exercise hereof.

“Warrant Shares” means the shares of Common Stock or other securities issuable upon exercise of the Warrants.

“Warrants” means this Warrant and all warrants issued upon transfer, division or combination of, or in substitution for, any thereof. All Warrants shall at all times be identical as to terms and conditions and date, except as to the number of shares of Common Stock for which they may be exercised.

2. Exercise of Warrant.

2.1 Manner of Exercise. From and after the Closing Date, and until 5:00 P.M., New York time, on the Expiration Date (the “Exercise Period”), the Holder may exercise this Warrant, on any Business Day, for all or any part of the number of Warrant Shares then purchasable hereunder.

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In order to exercise this Warrant, in whole or in part, the Holder shall deliver to the Company at its principal office or at the office or agency designated by the Company pursuant to Section 12, (i) a written notice of Holder’s election to exercise this Warrant, which notice shall specify the number of shares of Warrant Stock to be purchased, (ii) payment of the Warrant Price as provided herein, and (iii) this Warrant. Such notice shall be substantially in the form of the subscription form appearing at the end of this Warrant as Exhibit A, duly executed by the Holder or its agent or attorney (the “Exercise Notice”). Upon receipt thereof, the Company shall, as promptly as practicable, and in any event within three Business Days thereafter, execute or cause to be executed and deliver or cause to be delivered to the Holder a certificate or certificates representing the aggregate number of full shares of Warrant Stock issuable upon such exercise, together with an additional full share of Common Stock in lieu of any fraction of a share, as hereinafter provided. The stock certificate or certificates so delivered shall be, to the extent possible, in such denomination or denominations as the Holder shall request in the notice and shall be registered in the name of the Holder or such other name as shall be designated in the notice. This Warrant shall be deemed to have been exercised and such certificate or certificates shall be deemed to have been issued, and the Holder or any other Person so designated to be named therein shall be deemed to have become a Holder of record of such shares for all purposes, as of the date when the notice, together with the payment of the Warrant Price and this Warrant, is received by the Company as described above. If this Warrant shall have been exercised in part, the Company shall, at the time of delivery of the certificate or certificates representing Warrant Stock, deliver to the Holder a new Warrant evidencing the rights of the Holder to purchase the unpurchased Warrant Shares called for by this Warrant, which new Warrant shall in all other respects be identical with this Warrant, or at the request of the Holder, appropriate notation may be made on this Warrant and the same returned to the Holder.

The Holder may pay the Warrant Price in either of the following forms or, at the election of Holder, a combination thereof:

(a) through a cash exercise by payment of immediately available funds in the form of (i) a certified or official bank check payable to the order of the Company or (ii) wire transfer to the account of the Company, or

(b) if at any time after the first year following the Closing Date, an effective Registration Statement is not available for the resale of all of the Warrant Stock issuable hereunder at the time an Exercise Notice is delivered to the Company, through a cashless exercise (a “Cashless Exercise”). The Holder may effect a Cashless Exercise by surrendering this Warrant to the Company and noting on the Exercise Notice that the Holder wishes to effect a Cashless Exercise, upon which the Company shall issue to the Holder the number of shares of Warrant Stock determined as follows:

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2.2 Fractional Shares. The Company shall not be required to issue a fractional share of Common Stock upon exercise of any Warrant. As to any fraction of a share which the Holder of one or more Warrants, the rights under which are exercised in the same transaction, would otherwise be entitled to purchase upon such exercise, the Company shall deliver an additional full share of Common Stock in lieu of such fractional share.

2.3 Continued Rights. A holder of shares of Warrant Stock issued upon the exercise of this Warrant (other than a holder who acquires such shares after the same have been publicly sold pursuant to an effective registration statement (as defined in the Investor Rights Agreement referred to in Section 9 below) under the Securities Act or sold pursuant to Rule 144 thereunder), shall continue to be entitled with respect to such shares to all rights to which it would have been entitled as the Holder under Sections 10 and 13 of this Warrant.

2.4 Restrictions on Exercise Amount.

In the event the Company is prohibited at any time from issuing shares of Warrant Stock as a result of any restrictions or prohibitions under applicable law or the rules or regulations of any stock exchange, interdealer quotation system or other self-regulatory organization, the Company shall as soon as possible seek the approval of its stockholders and take such other action to authorize the issuance of the full number of shares of Common Stock issuable upon exercise of this Warrant.

3. Transfer, Division and Combination.

3.1 Transfer. The Warrants and the Warrant Stock shall be freely transferable, subject to compliance with all applicable laws, including, but not limited to the Securities Act. If, at the time of the surrender of this Warrant in connection with any transfer of this Warrant or the resale of the Warrant Stock, this Warrant or the Warrant Stock, as applicable, shall not be registered under the Securities Act, the Company may require, as a condition of allowing such transfer (i) that the Holder or transferee of this Warrant or the Warrant Stock, as the case may be, furnish to the Company a written opinion of counsel that is reasonably acceptable to the Company to the effect that such transfer may be made without registration under the Securities Act, (ii) that the Holder or transferee execute and deliver to the Company an investment letter in form and substance acceptable to the Company and substantially in the form attached as Exhibit C hereto and (iii) that the transferee be an “accredited investor” as defined in Rule 501(a) promulgated under the Securities Act. Transfer of this Warrant and all rights hereunder, in whole or in part, in accordance with the foregoing provisions, shall be registered on the books of the Company to be maintained for such purpose, upon surrender of this Warrant at the principal office of the Company referred to in Section 2.1 or the office or agency designated by the Company pursuant to Section 12, together with a written assignment of this Warrant substantially in the form of Exhibit B hereto duly executed by the Holder or its agent or attorney and funds sufficient to pay any transfer taxes payable upon the making of such transfer. Upon such surrender and, if

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required, such payment, the Company shall as promptly as practicable and in any event within five Business Days execute and deliver a new Warrant or Warrants in the name of the assignee or assignees and in the denomination specified in such instrument of assignment, and shall issue to the assignor a new Warrant evidencing the portion of this Warrant not so assigned, and this Warrant shall promptly be cancelled. Following a transfer that complies with the requirements of this Section 3.1, the Warrant may be exercised by a new Holder for the purchase of shares of Common Stock regardless of whether the Company issued or registered a new Warrant on the books of the Company.

3.2 Restrictive Legends. Each certificate for Warrant Stock initially issued upon the exercise of this Warrant, and each certificate for Warrant Stock issued to any subsequent transferee of any such certificate, unless, in each case, such Warrant Stock is eligible for resale without registration pursuant to Rule 144(k) under the Exchange Act or such Warrant Stock has been sold pursuant to an effective registration statement under the Securities Act, shall be stamped or otherwise imprinted with a legend in substantially the following form:

“THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE OFFERED, SOLD, ASSIGNED OR TRANSFERRED, IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER SAID ACT OR UNLESS THE COMPANY HAS RECEIVED AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE COMPANY THAT REGISTRATION UNDER SAID ACT IS NOT REQUIRED.”

3.3 Division and Combination; Expenses; Books. This Warrant may be divided or combined with other Warrants upon presentation hereof at the aforesaid office or agency of the Company, together with a written notice specifying the names and denominations in which new Warrants are to be issued, signed by the Holder or its agent or attorney. Subject to compliance with Section 3.1 as to any transfer which may be involved in such division or combination, the Company shall execute and deliver a new Warrant or Warrants in exchange for the Warrant or Warrants to be divided or combined in accordance with such notice and Section 3.1. The Company shall prepare, issue and deliver at its own expense the new Warrant or Warrants under this Section 3. The Company agrees to maintain, at its aforesaid office or agency, books for the registration and the registration of transfer of the Warrants.

4. Adjustments. The number of Warrant Shares and the Current Warrant Price shall be subject to adjustment from time to time as set forth in this Section 4. The Company shall give the Holder notice of any event described below which requires an adjustment pursuant to this Section 4 in accordance with Section 5.

4.1 Stock Dividends, Subdivisions and Combinations. If at any time while this Warrant is outstanding the Company shall:

(i) declare a dividend or make a distribution on its outstanding shares of Common Stock in shares of Common Stock,

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(ii) subdivide its outstanding shares of Common Stock into a larger number of shares of Common Stock, or

(iii) combine its outstanding shares of Common Stock into a smaller number of shares of Common Stock, then:

(1) the number of shares of Common Stock acquirable upon exercise of this Warrant immediately after the occurrence of any such event shall be adjusted to equal the number of shares of Common Stock which a record holder of the same number of shares of Common Stock that would have been acquirable under this Warrant immediately prior to the record date for such dividend or distribution or the effective date of such subdivision or combination would own or be entitled to receive after such record date or the effective date of such subdivision or combination, as applicable, and

(2) the Current Warrant Price shall be adjusted to equal:

(A) the Current Warrant Price in effect at the time of the record date for such dividend or distribution or of the effective date of such subdivision or combination, multiplied by the number of shares of Common Stock into which this Warrant is exercisable immediately prior to the adjustment, divided by

(B) the number of shares of Common Stock into which this Warrant is exercisable immediately after such adjustment.

Any adjustment made pursuant to clause (i) of this paragraph shall become effective immediately after the record date for the determination of stockholders entitled to receive such dividend or distribution, and any adjustment pursuant to clauses (ii) or (iii) of this paragraph shall become effective immediately after the effective date of such subdivision or combination.

4.2 Certain Other Distributions. If at any time while this Warrant is outstanding the Company shall cause the holders of its Common Stock to be entitled to receive any dividend or other distribution of:

(i) cash,

(ii) any evidences of its indebtedness, any shares of stock of any class or any other securities or property or assets of any nature whatsoever (other than cash or additional shares of Common Stock as provided in Section 4.1 hereof), or

(iii) any warrants or other rights to subscribe for or purchase any evidences of its indebtedness, any shares of stock of any class or any other securities or property or assets of any nature whatsoever, then:

(1) the number of shares of Common Stock acquirable upon exercise of this Warrant shall be adjusted to equal the product of the number of shares of Common Stock acquirable upon exercise of this Warrant immediately prior to the record date for such dividend or distribution, multiplied by a fraction (x) the numerator of which shall be the Current Warrant Price at the date of taking such record and (y) the denominator of which shall be such Current Warrant Price

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minus the amount allocable to one share of Common Stock of any such cash so distributable and of the fair value (as determined in good faith by the Board of Directors of the Company) of any and all such evidences of indebtedness, shares of stock, other securities or property or warrants or other subscription or purchase rights so distributable; and

(2) the Current Warrant Price in effect immediately prior to the record date fixed for determination of stockholders entitled to receive such distribution shall be adjusted to equal (x) the Current Warrant Price multiplied by the number of shares of Common Stock acquirable upon exercise of this Warrant immediately prior to the adjustment, divided by (y) the number of shares of Common Stock acquirable upon exercise of this Warrant immediately after such adjustment.

(3) a reclassification of the Common Stock (other than a change in par value, or from par value to no par value or from no par value to par value) into shares of Common Stock and shares of any other class of stock shall be deemed a distribution by the Company to the holders of its Common Stock of such shares of such other class of stock within the meaning of this Section 4.2 and, if the outstanding shares of Common Stock shall be changed into a larger or smaller number of shares of Common Stock as a part of such reclassification, such change shall be deemed a subdivision or combination, as the case may be, of the outstanding shares of Common Stock within the meaning of Section 4.1.

4.3 Adjustment for Dilutive Issuances. If the Company shall issue any shares of Common Stock, or shall issue any Common Stock Equivalents (as defined below), for a consideration per share less than the Current Warrant Price then in effect immediately prior to the issuance of such Common Stock or Common Stock Equivalents, then, except as provided for in clause (iv) below, the Current Warrant Price in effect immediately prior to each such issuance shall be decreased to the amount determined in accordance with the following formula:

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No further adjustment to the Current Warrant Price shall be made upon the subsequent issue of shares of Common Stock upon the exercise, conversion or exchange of any Common Stock Equivalents.

For purpose of any adjustment of the Current Warrant Price pursuant to this Section 4.3, the following provisions shall be applicable:

(i) The per share consideration for the sale or issuance of Common Stock Equivalents shall be the price per share received by the Company before payment of commissions, discounts and other expenses. The value of any non-cash consideration received or receivable upon the sale or issuance of Common Stock or Common Stock Equivalents shall be determined in good faith by the Board of Directors of the Company.

(ii) In the case of the sale or issuance of Common Stock Equivalents, the per share consideration shall be determined by dividing the maximum number of shares of Common Stock issuable with respect to such Common Stock Equivalents into the aggregate consideration received by the Company upon the sale of issuance of such Common Stock Equivalents plus the minimum aggregate amount of any additional consideration receivable by the Company upon the conversion or exercise of such Common Stock Equivalents. Such maximum number of shares shall be deemed issued on the earlier of the payment date or record date for a distribution of Common Stock Equivalents.

(iii) If any Common Stock Equivalents included in adjustments under this Section 4.3 expire or terminate without the Common Stock to which they related having been issued, the Current Warrant Price shall be readjusted to eliminate the effect of the assumed issuance of such Common Stock. If any Common Stock Equivalents by their terms provide for subsequent increases in the additional consideration payable for the related Common Stock or for subsequent decreases in the number of shares of Common Stock obtainable, upon any such increase or decrease, the Current Warrant Price shall be appropriately readjusted to the extent such Common Stock Equivalents have not then expired or been exercised or converted. The aggregate increase in the Current Warrant Price caused by all such readjustments shall not exceed the decrease in Current Warrant Price made upon the issuance of the Common Stock Equivalents to which such readjustment relates.

(iv) The following issuances of Common Stock or Common Stock Equivalents shall be excluded from the adjustment of the Current Warrant Price: (A) any dividend or distribution on the Common Stock for which adjustment of the Current Warrant Price is made pursuant to Sections 4.1 or 4.2; (B) shares of Common Stock issued to, or issuable upon exercise of Common Stock Equivalents issued to, employees, directors, consultants or advisors of the Company pursuant to a plan approved by the Board of Directors of the Company; (C) shares of Common Stock or Common Stock Equivalents issued as dividends on, or otherwise pursuant to, the Company’s 15% Senior Redeemable Convertible Preferred Stock, 20% Junior Redeemable Convertible Preferred Stock or pursuant to other Common Stock Equivalents outstanding at the Closing Date; or (D) shares of Common Stock or Common Stock Equivalents issued to lenders to the Company or purchasers of its debt securities in bona fide financing transactions that principally involve the incurrence of indebtedness for money borrowed.

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4.4 Other Provisions Applicable to Adjustments. The following provisions shall be applicable to the making of adjustments of the number of Warrant Shares and the Current Warrant Price provided for in Section 4:

(a) When Adjustments to Be Made. The adjustments required by Section 4 shall be made whenever and as often as any specified event requiring an adjustment shall occur, except that any that would otherwise be required may be postponed (except in the case of a subdivision or combination of shares of the Common Stock, as provided for in Section 4.1) up to, but not beyond, the date of exercise if such adjustment either by itself or with other adjustments not previously made adds or subtracts less than 1% of the shares of Common Stock into which this Warrant is exercisable immediately prior to the making of such adjustment. Any adjustment representing a change of less than such minimum amount (except as aforesaid) which is postponed shall be carried forward and made as soon as such adjustment, together with other adjustments required by this Section 4 and not previously made, would result in a minimum adjustment or on the date of exercise, whichever is earlier.

(b) Fractional Interests. In computing adjustments under this Section 4, fractional interests in Common Stock shall be taken into account to the nearest 1/100th of a share.

(c) When Adjustment Not Required. If the Company undertakes a transaction contemplated under this Section 4 and as a result takes a record of the holders of its Common Stock for the purpose of entitling them to receive a dividend or distribution or subscription or purchase rights or other benefits contemplated under this Section 4 and shall, thereafter and before the distribution to stockholders thereof, legally abandon its plan to pay or deliver such dividend, distribution, subscription or purchase rights or other benefits contemplated under this Section 4, then thereafter no adjustment shall be required by reason of the taking of such record and any such adjustment previously made in respect thereof shall be rescinded and annulled.

(d) Escrow of Distribution. If after any property becomes distributable pursuant to Section 4 by reason of the taking of any record of the holders of Common Stock, but prior to the occurrence of the event for which such record is taken, a Holder of this Warrant exercises the Warrant during such time, then such Holder shall continue to be entitled to receive any shares of Common Stock issuable upon exercise hereunder by reason of such adjustment and such shares or other property shall be held in escrow for the Holder of this Warrant by the Company to be issued to the Holder of this Warrant upon and to the extent that the event actually takes place. Notwithstanding any other provision to the contrary herein, if the event for which such record was taken fails to occur or is rescinded, then such escrowed shares shall be canceled by the Company and escrowed property returned to the Company.

4.5 Reorganization, Reclassification, Merger, Consolidation or Disposition of Assets. If there shall occur a Change of Control which is approved by the Company’s Board of Directors, then the Holder of this Warrant shall be entitled, at such Holder’s option, either:

(a) if pursuant to the terms of the transaction that constitutes such Change of Control, shares of common stock of the successor or acquiring entity, or any cash, shares of stock or other securities or property of any nature whatsoever (including warrants or other subscription or purchase rights) in addition to or in lieu of common stock or other equity interests of the

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successor or acquiring entity (“Other Property”), are to be received by or distributed to the holders of Common Stock of the Company, then the Holder of this Warrant shall have the right thereafter to receive, upon the exercise of the Warrant, the number of shares of common stock or other equity interests of the successor or acquiring entity or of the Company, if it is the surviving corporation, and the Other Property receivable upon or as a result of such Change of Control by a holder of the number of shares of Common Stock into which this Warrant is exercisable immediately prior to such event; or

(b) In case of any transaction that constitutes such Change of Control described above, the successor or acquiring entity (if other than the Company) and, if an entity different from the successor or surviving entity, the entity whose capital stock or assets the holders of Common Stock are entitled to receive as a result of such transaction, shall expressly assume the due and punctual observance and performance of each and every covenant and condition contained in this Warrant to be performed and observed by the Company and all the obligations and liabilities hereunder, subject to such modifications as may be deemed appropriate (as determined by resolution of the Board of Directors of the Company prior to such Change of Control) in order to provide for adjustments of shares of the Common Stock into which this Warrant is exercisable which shall be as nearly equivalent as practicable to the adjustments provided for in Section 4. For purposes of Section 4, common stock or other equity interests of the successor or acquiring entity shall include stock of such corporation of any class which is not preferred as to dividends or assets on liquidation over any other class of stock or other equity interests of such entity and which is not subject to redemption and shall also include any evidences of indebtedness, shares of stock or other securities which are convertible into or exchangeable for any such stock, either immediately or upon the arrival of a specified date or the happening of a specified event and any warrants or other rights to subscribe for or purchase any such stock or other equity interests. The foregoing provisions of this Section 4 shall similarly apply to successive Change of Control transactions.

4.6 Other Action Affecting Common Stock. In case at any time or from time to time the Company shall take any action in respect of its Common Stock, other than the payment of dividends described in Section 4 or any other action described in Section 4, then, unless such action will not have a materially adverse effect upon the rights of the Holder of this Warrant, the number of Warrant Shares for which this Warrant is exercisable and/or the purchase price thereof shall be adjusted in such manner as may be equitable in the circumstances.

4.7 Certain Limitations. Notwithstanding anything herein to the contrary, (a) the Company agrees not to enter into any transaction which, by reason of any adjustment hereunder, would cause the Current Warrant Price to be less than the par value per share of Common Stock and (b) in no event, by reason of any adjustment under Sections 4.2 and/or 4.3, prior to any necessary approval referred to in Section 2.4 will the number of shares of Common Stock into which the Warrant is exercisable exceed such number equal to 19.9% of the shares of Common Stock outstanding at the Time of Sale.

4.8 Stock Transfer Taxes. The issue of stock certificates upon exercise of this Warrant shall be made without charge to the Holder for any tax in respect of such issue. The Company shall not, however, be required to pay any tax which may be payable in respect of any transfer involved in the issue and the delivery of shares in any name other than that of the

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Holder, and the Company shall not be required to issue or deliver any such stock certificate unless and until the Person or Persons requesting the issue thereof shall have paid to the Company the amount of such tax or shall have established to the satisfaction of the Company that such tax has been paid.

5. Notices to Warrant Holders.

5.1 Certificate as to Adjustments. Upon the occurrence of each adjustment or readjustment of the number of Warrant Shares or Current Warrant Price, the Company, at its expense, shall promptly compute such adjustment or readjustment in accordance with the terms hereof and prepare and furnish to the Holder a certificate setting forth such adjustment or readjustment and showing in detail the facts upon which such adjustment or readjustment is based. The Company shall, upon the written request at any time of the Holder of this Warrant, furnish or cause to be furnished to such Holder a like certificate setting forth (i) such adjustments and readjustments, (ii) the Current Warrant Price at the time in effect and (iii) the number of shares of Common Stock and the amount, if any, or other property which at the time would be received upon the exercise of Warrants owned by such Holder.

5.2 Notice of Corporate Action. If at any time:

(a) the Company shall take a record of the holders of its Common Stock for the purpose of entitling them to receive a dividend (other than a cash dividend payable out of earnings or earned surplus legally available for the payment of dividends under the laws of the jurisdiction of incorporation of the Company) or other distribution, or any right to subscribe for or purchase any evidences of its indebtedness, any shares of stock of any class or any other securities or property, or to receive any other right, or

(b) there shall be any capital reorganization of the Company, any reclassification or recapitalization of the capital stock of the Company or any consolidation or merger of the Company with, or any sale, transfer or other disposition of all or substantially all the property, assets or business of the Company to, another entity, or

(c) there shall be a voluntary or involuntary dissolution, liquidation or winding up of the Company;

then, in any one or more of such cases, the Company shall give to the Holder (i) at least 20 days’ prior written notice of the date on which a record date shall be selected for such dividend, distribution or right or for determining rights to vote in respect of any such reorganization, reclassification, merger, consolidation, sale, transfer, disposition, dissolution, liquidation or winding up, and (ii) in the case of any such reorganization, reclassification, merger, consolidation, sale, transfer, disposition, dissolution, liquidation or winding up, at least 20 days’ prior written notice of the date when the same shall take place. Such notice in accordance with the foregoing clause also shall specify (x) the date on which any such record is to be taken for the purpose of such dividend, distribution or right, the date on which the holders of Common Stock shall be entitled to any such dividend, distribution or right, and the amount and character thereof, and (y) the date on which any such reorganization, reclassification, merger, consolidation, sale, transfer, disposition, dissolution, liquidation or winding up is to take place

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and the time, if any such time is to be fixed, as of which the holders of Common Stock shall be entitled to exchange their shares of Common Stock for securities or other property deliverable upon such reorganization, reclassification, merger, consolidation, sale, transfer, disposition, dissolution, liquidation or winding up. Each such written notice shall be sufficiently given if addressed to the Holder at the last address of the Holder appearing on the books of the Company and delivered in accordance with Section 15.2.

5.3 No Rights as Stockholder. This Warrant does not entitle the Holder to any voting or other rights as a stockholder of the Company prior to exercise and payment of the Warrant Price in accordance with the terms hereof.

6. No Impairment. The Company shall not by any action, including, without limitation, amending its certificate of incorporation or through any reorganization, transfer of assets, consolidation, merger, dissolution, issue or sale of securities or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms of this Warrant, but will at all times in good faith assist in the carrying out of all such terms and in the taking of all such actions as may be necessary or appropriate to protect the rights of the Holder against impairment. Without limiting the generality of the foregoing, the Company will (a) not increase the par value of any shares of Common Stock receivable upon the exercise of this Warrant above the amount payable therefor upon such exercise immediately prior to such increase in par value, (b) take all such action as may be necessary or appropriate in order that the Company may validly and legally issue fully paid and nonassessable shares of Common Stock upon the exercise of this Warrant, and (c) use its reasonable best efforts to obtain all such authorizations, exemptions or consents from any public regulatory body having jurisdiction thereof as may be necessary to enable the Company to perform its obligations under this Warrant. Upon the request of the Holder, the Company will at any time during the period this Warrant is outstanding acknowledge in writing, in form satisfactory to the Holder, the continuing validity of this Warrant and the obligations of the Company hereunder.

7. Reservation and Authorization of Common Stock; Registration With Approval of Any Governmental Authority. From and after the Closing Date, the Company shall at all times reserve and keep available for issue upon the exercise of Warrants such number of its authorized but unissued shares of Common Stock as will be sufficient to permit the exercise in full of all outstanding Warrants (without regard to any ownership limitations provided in Section 2.4(i)). All shares of Common Stock which shall be so issuable, when issued upon exercise of any Warrant and payment therefor in accordance with the terms of such Warrant, shall be duly and validly issued and fully paid and nonassessable, and not subject to preemptive rights. Before taking any action which would cause an adjustment reducing the Current Warrant Price below the then par value, if any, of the shares of Common Stock issuable upon exercise of the Warrants, the Company shall take any corporate action which may be necessary in order that the Company may validly and legally issue fully paid and non-assessable shares of such Common Stock at such adjusted Current Warrant Price. Before taking any action which would result in an adjustment in the number of shares of Common Stock for which this Warrant is exercisable or in the Current Warrant Price, the Company shall obtain all such authorizations or exemptions thereof, or consents thereto, as may be necessary from any public regulatory body or bodies having jurisdiction thereof. If any shares of Common Stock required to be reserved for issuance upon exercise of Warrants require registration or qualification with any governmental authority

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under any federal or state law before such shares may be so issued (other than as a result of a prior or contemplated distribution by the Holder of this Warrant), the Company will in good faith and as expeditiously as possible and at its expense endeavor to cause such shares to be duly registered.

8. Taking of Record; Stock and Warrant Transfer Books. In the case of all dividends or other distributions by the Company to the holders of its Common Stock with respect to which any provision of Section 4 refers to the taking of a record of such holders, the Company will in each such case take such a record and will take such record as of the close of business on a Business Day. The Company will not at any time, except upon dissolution, liquidation or winding up of the Company, close its stock transfer books or Warrant transfer books so as to result in preventing or delaying the exercise or transfer of any Warrant.

9. Registration Rights. The resale of the Warrant Stock shall be registered in accordance with the terms and conditions contained in that certain Investor Rights Agreement dated of even date hereof, among the Holder and the Company (the “Investor Rights Agreement”). The Holder acknowledges that pursuant to the Investor Rights Agreement, the Company has the right to request that the Holder furnish information regarding such Holder and the distribution of the Warrant Stock as is required by law or the Commission to be disclosed in the Registration Statement (as such term is defined in the Investor Rights Agreement), and the Company may exclude from such registration the shares of Warrant Stock acquirable hereunder if Holder fails to furnish such information within a reasonable time prior to the filing of each registration statement, supplemental prospectus included therein and/or amended registration statement.

10. Supplying Information. Upon any default by the Company of its obligations hereunder or under the Investor Rights Agreement, the Company shall cooperate with the Holder in supplying such information as may be reasonably necessary for such Holder to complete and file any information reporting forms presently or hereafter required by the Commission as a condition to the availability of an exemption from the Securities Act for the sale of any Warrant or Warrant Stock.

11. Loss or Mutilation. Upon receipt by the Company from the Holder of evidence reasonably satisfactory to it of the ownership of and the loss, theft, destruction or mutilation of this Warrant and a contractual indemnity reasonably satisfactory to it and reimbursement to the Company of all reasonable expenses incidental thereto and in case of mutilation upon surrender and cancellation hereof, the Company will execute and deliver in lieu hereof a new Warrant of like tenor to the Holder; provided, however, that in the case of mutilation, no indemnity shall be required if this Warrant in identifiable form is surrendered to the Company for cancellation.

12. Office of the Company. As long as any of the Warrants remain outstanding, the Company shall maintain an office or agency (which may be the principal executive offices of the Company) where the Warrants may be presented for exercise, registration of transfer, division or combination as provided in this Warrant.

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13. Financial and Business Information.

13.1 Quarterly Information. The Company will deliver to the Holder, as soon as available and in any event within 45 days after the end of each of the first three quarters of each fiscal year of the Company, one copy of an unaudited consolidated balance sheet of the Company and its subsidiaries as at the end of such quarter, and the related unaudited consolidated statements of income and cash flow of the Company and its subsidiaries for such quarter and, in the case of the second and third quarters, for the portion of the fiscal year ending with such quarter, setting forth in each case in comparative form the figures for the corresponding periods in the previous fiscal year. Such financial statements shall be prepared by the Company in accordance with GAAP and accompanied by the certification of the Company’s chief executive officer or chief financial officer that such financial statements present fairly the consolidated financial position, results of operations and cash flow of the Company and its subsidiaries as at the end of such quarter and for such year-to-date period, as the case may be; provided, however, that the Company shall have no obligation to deliver such quarterly information under this Section 13.1 to the extent it is publicly available; and provided further, that if such information contains material non-public information, the Company shall so notify the Holder prior to delivery thereof and the Holder shall have the right to refuse delivery of such information.

13.2 Annual Information. The Company will deliver to the Holder as soon as available and in any event within 90 days after the end of each fiscal year of the Company, one copy of an audited consolidated balance sheet of the Company and its subsidiaries as at the end of such year, and audited consolidated statements of income, retained earnings and cash flow of the Company and its subsidiaries for such year; setting forth in each case in comparative form the figures for the corresponding periods in the previous fiscal year; all prepared in accordance with GAAP, and which audited financial statements shall be accompanied by an opinion thereon of the independent certified public accountants regularly retained by the Company, or any other firm of independent certified public accountants of recognized national standing selected by the Company; provided, however, that the Company shall have no obligation to deliver such annual information under this Section 13.2 to the extent it is publicly available; and provided further, that if such information contains material non-public information, the Company shall so notify the Holder prior to delivery thereof and the Holder shall have the right to refuse delivery of such information.

13.3 Filings. The Company will file on or before the required date all regular or periodic reports (pursuant to the Exchange Act) with the Commission.

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14. Limitation of Liability. No provision hereof, in the absence of affirmative action by the Holder to purchase shares of Common Stock, and no enumeration herein of the rights or privileges of the Holder hereof, shall give rise to any liability of the Holder for the purchase price of any Common Stock, whether such liability is asserted by the Company or by creditors of the Company.

15. Miscellaneous.

15.1 Nonwaiver and Expenses. No course of dealing or any delay or failure to exercise any right hereunder on the part of the Holder shall operate as a waiver of such right or otherwise prejudice Holder’s rights, powers or remedies. If the Company fails to make, when due, any payments provided for hereunder, or fails to comply with any other provision of this Warrant, the Company shall pay to the Holder such amounts as shall be sufficient to cover any third party costs and expenses including, but not limited to, reasonable attorneys’ fees, including those of appellate proceedings, incurred by the Holder in collecting any amounts due pursuant hereto or in otherwise enforcing any of its rights, powers or remedies hereunder.

15.2 Notice Generally. Any and all notices or other communications or deliveries required or permitted to be provided hereunder shall be in writing and shall be deemed given and effective on the earliest of (a) the date of transmission, if such notice or communication is delivered via facsimile at the facsimile number specified in this Section prior to 5:00 p.m. (Houston time) on a Business Day, (b) the next Business Day after the date of transmission, if such notice or communication is delivered via facsimile at the facsimile number specified in this Section on a day that is not a Business Day or later than 5:00 p.m. (Houston time) on any Business Day, or (c) the Business Day following the date of mailing, if sent by U.S. nationally recognized overnight courier service such as Federal Express. The address for such notices and communications shall be as follows:

If to the Holder, addressed to:

with a copy to:

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or with respect to the Company, addressed to:

Transmeridian Exploration Incorporated

397 N. Sam Houston Pkwy E, Suite 300

Houston, Texas 77060

Attention: General Counsel

Facsimile No.: 281 ###-###-####

or to such other address or addresses or facsimile number or numbers as any such party may most recently have designated in writing to the other parties hereto by such notice.

Unless otherwise stated above, such communications shall be effective when they are received by the addressee thereof in conformity with this section. Any party may change its address for such communications by giving notice thereof to the other parties in conformity with this section.

15.3 Successors and Assigns. Subject to compliance with the provisions of Section 3.1, this Warrant and the rights evidenced hereby shall inure to the benefit of and be binding upon the successors of the Company and the successors and assigns of the Holder. The provisions of this Warrant are intended to be for the benefit of all Holders from time to time of this Warrant, and shall be enforceable by any such Holder.

15.4 Amendment. This Warrant may be modified or amended or the provisions of this Warrant waived with the written consent of both the Company and the Holder.

15.5 Severability. Wherever possible, each provision of this Warrant shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Warrant shall be prohibited by or invalid under applicable law, such provision shall be modified to the extent of such prohibition or invalidity, without invalidating the remainder of such provision or the remaining provisions of this Warrant.

15.6 Headings. The headings used in this Warrant are for the convenience of reference only and shall not, for any purpose, be deemed a part of this Warrant.

15.7 Governing Law. This Warrant and the transactions contemplated hereby shall be deemed to be consummated in the State of Texas and shall be governed by and interpreted in accordance with the local laws of the State of Texas without regard to the provisions thereof relating to conflicts of laws. The Company hereby irrevocably consents to the non-exclusive jurisdiction of the State and Federal courts located in Houston, Texas in connection with any action or proceeding arising out of or relating to this Warrant. In any such litigation the Company agrees that the service thereof may be made by certified or registered mail directed to the Company pursuant to Section 15.2.

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IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by its duly authorized officers.

Dated: July 9, 2007

Signature Page to Common Stock Purchase

Warrant dated July 9, 2007

EXHIBIT A

SUBSCRIPTION FORM

[To be executed only upon exercise of Warrant]

1. The undersigned hereby elects to purchase shares of the Common Stock of Transmeridian Exploration Incorporated pursuant to the terms of the attached Warrant, and tenders herewith payment of the purchase price of such shares in full.

2. The undersigned hereby elects to convert the attached Warrant into Common Stock of Transmeridian Exploration Incorporated through “cashless exercise” in the manner specified in the Warrant. This conversion is exercised with respect to                      of the Shares covered by the Warrant.

3. Please issue a certificate or certificates representing said shares in the name of the undersigned or in such other name as is specified below:

[and, if such shares of Common Stock shall not include all of the shares of Common Stock issuable as provided in this Warrant, that a new Warrant of like tenor and date for the balance of the shares of Common Stock issuable hereunder be delivered to the undersigned.]

NOTICE: The signature on this subscription must correspond with the name as written upon the face of the Warrant in every particular, without alteration or enlargement or any change whatsoever.

A-1

EXHIBIT B

ASSIGNMENT FORM

FOR VALUE RECEIVED the undersigned registered owner of this Warrant for the purchase of shares of Common Stock of Transmeridian Exploration Incorporated hereby sells, assigns and transfers unto the Assignee named below all of the rights of the undersigned under this Warrant, with respect to the number of shares of Common Stock set forth below:

and does hereby irrevocably constitute and appoint                                                                                   attorney-in-fact to register such transfer on the books of the Company, maintained for the purpose, with full power of substitution in the premises.

NOTICE: The signature on this assignment must correspond with the name as written upon the face of the Warrant in every particular, without alteration or enlargement or any change whatsoever.

B-1

EXHIBIT C

FORM OF INVESTMENT REPRESENTATION LETTER

In connection with the acquisition of [warrants (the “Warrants”) to purchase                      shares of common stock of Transmeridian Exploration Incorporated (the “Company”), par value $0.0006 per share (the “Common Stock”)][                     shares of common stock of Transmeridian Exploration Incorporated (the “Company”), par value $0.0006 per share (the “Common Stock”) upon the exercise of warrants by                     ], by                      (the “Holder”) from                     , the Holder hereby represents and warrants to the Company as follows:

The Holder (i) is an “Accredited Investor” as that term is defined in Rule 501 of Regulation D promulgated under the Securities Act of 1933, as amended (the “Act”); and (ii) has the ability to bear the economic risks of such Holder’s prospective investment, including a complete loss of Holder’s investment in the Warrants and the shares of Common Stock issuable upon the exercise thereof (collectively, the “Securities”).

The Holder, by acceptance of the Warrants, represents and warrants to the Company that the Warrants and all securities acquired upon any and all exercises of the Warrants are purchased for the Holder’s own account, and not with view to distribution of either the Warrants or any securities purchasable upon exercise thereof in violation of applicable securities laws.

The Holder acknowledges that (i) the Securities have not been registered under the Act, (ii) the Securities are “restricted securities” and the certificate(s) representing the Securities shall bear the following legend, or a similar legend to the same effect, until (i) in the case of the shares of Common Stock underlying the Warrants, such shares shall have been registered for resale by the Holder under the Act and effectively been disposed of in accordance with a registration statement that has been declared effective; or (ii) in the opinion of counsel reasonably acceptable to the Company such Securities may be sold without registration under the Act:

“[NEITHER] THE SECURITIES REPRESENTED BY THIS CERTIFICATE [NOR THE SECURITIES INTO WHICH THEY ARE EXERCISABLE] HAVE [NOT] BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), AND ALL SUCH SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AS SET FORTH IN THIS CERTIFICATE. [NEITHER] THE SECURITIES REPRESENTED HEREBY [NOR THE SECURITIES INTO WHICH THEY ARE EXERCISABLE] MAY [NOT] BE SOLD, TRANSFERRED, OR OTHERWISE DISPOSED OF IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER THE ACT OR AN OPINION OF COUNSEL, REASONABLY ACCEPTABLE TO COUNSEL FOR THE COMPANY, TO THE EFFECT THAT THE PROPOSED SALE, TRANSFER, OR DISPOSITION MAY BE EFFECTUATED WITHOUT REGISTRATION UNDER THE ACT.”

C-1

IN WITNESS WHEREOF, the Holder has caused this Investment Representation Letter to be executed in its corporate name by its duly authorized officer this      day of              20        .

C-2