AMENDMENT NO. 1 TO ESCROW AGREEMENT

Exhibit 10.1

EXECUTION VERSION

AMENDMENT NO. 1 TO ESCROW AGREEMENT

This Amendment No. 1 to Escrow Agreement (this “Amendment”), dated as of May 26, 2006, is among The Bank of New York, as escrow agent (in such capacity, the “Escrow Agent”), The Bank of New York, as Trustee under the Indenture (in such capacity, the “Trustee”) and Transmeridian Exploration Inc., an international business company incorporated under the laws of the British Virgin Islands (the “Company”) (collectively, the “Subject Parties”).

RECITALS

A. The Subject Parties are parties to that certain Escrow Agreement, dated as of December 12, 2005 (as heretofore amended or otherwise modified, the “Escrow Agreement”).

B. The Company and certain guarantors named therein executed and delivered to the Trustee an indenture dated as of December 12, 2005 (the “Initial Indenture”), as amended by the First Supplemental Indenture dated as of December 22, 2005 (the “First Supplemental Indenture”), relating to the Company’s Senior Secured Notes due 2010 issued on December 12, 2005 in the aggregate principal amount of $250,000,000 (the “Securities”). The Initial Indenture as amended and supplemented by the First Supplemental Indenture is referred to herein as the “Original Indenture.”

C. The Subject Parties and the Guarantors have entered into the Second Supplemental Indenture dated as of May 24, 2006 (the “Second Supplemental Indenture”) to amend and supplement the Original Indenture to provide for the issuance of an additional aggregate principal amount of $40,000,000 of the Company’s Senior Secured Notes due 2010 (the “Additional Securities”).

D. The Subject Parties have agreed to enter into this Amendment in accordance with Section 5 of the Second Supplemental Indenture to amend and modify the Escrow Agreement to provide, as security for the Company’s obligations under the Securities, the Additional Securities and the Indenture, the Additional Interest Escrow Amount (as defined herein) as additional Collateral (as defined in the Escrow Agreement) under the Escrow Agreement and to make certain other amendments thereto.

NOW, THEREFORE, in consideration of the premises and the respective representations, warranties, covenants and agreements set forth in this Amendment, and intending to be legally bound, the Subject Parties hereby agree as follows:

ARTICLE 1

DEFINITIONS; CONSTRUCTION

1.1 Defined Terms. Capitalized terms that are defined in this Amendment shall have the meanings ascribed in this Amendment to such terms. All other capitalized terms shall have the meanings ascribed to such terms in the Escrow Agreement, as amended by this Amendment.

1.2 Construction. Upon and after the execution of this Amendment, each reference in the Escrow Agreement to “this Agreement,” “hereunder,” “hereof” or words of like import referring to the “Agreement” shall be a reference to the Escrow Agreement as modified hereby.

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ARTICLE 2

AMENDMENTS

2.1 Amendments to the Escrow Agreement.

(a) The first paragraph (A) in the “RECITALS” of the Escrow Agreement is hereby amended by adding the underlined and bold language and deleting the struck out language below:

“Pursuant to the Indenture, dated as of December 12, 2005 (as amended or supplemented from time to time, the “Indenture”), among the Company, each of the Guarantors party thereto and the Trustee, the Company is issuing $290,000,000 aggregate principal amount of its Senior Secured Notes due 2010 (the “Securities”).”

(b) Section 1 “Defined Terms” of the Escrow Agreement is hereby amended by:

(i) adding the following new defined terms:

“ “Additional Interest Escrow Amount” means $3,600,000.”

“Additional Issue Date” means the date on which the Additional Securities are first issued under the Indenture.”

(ii) amending and restating the defined term “Available Funds” by adding the underlined and bold language below:

“ “Available Funds” means (i) the sum of (A) the Initial Interest Escrow Amount, (B) the Additional Interest Escrow Amount, (C) the Initial Bramex Escrow Amount and (D) interest earned or dividends paid on the funds in the Escrow Account (including holdings of U.S. Government Securities), less (ii) the aggregate disbursements previously made pursuant to this Escrow Agreement, which shall constitute at any time of determination all monies on deposit and/or securities credited to the Escrow Account.”

(c) Section 2(b) “Establishment of Escrow Account” is hereby amended by adding the following sentence at the end of the paragraph:

“On the Additional Issue Date, the Company will deliver the Additional Interest Escrow Amount to the Escrow Agent for deposit into the Escrow Account against the Escrow Agent’s written acknowledgment and receipt of the Additional Interest Escrow Amount.”

ARTICLE 3

MISCELLANEOUS

3.1 Security Interest. The Company hereby confirms its grant to the Trustee, for the ratable benefit of the Beneficiaries (including the Holders of the Additional Securities), pursuant to Section 6 of the Escrow Agreement of a first priority security interest in and lien upon the Collateral, including the Additional Interest Escrow Amount, to secure all obligations and indebtedness of the Company under the Indenture, the Securities and the Additional Securities.

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3.2 No Other Amendments; Reservation of Rights; No Waiver. Other than as otherwise expressly provided herein, this Amendment shall not be deemed to operate as an amendment or waiver of, or to prejudice, any right, power, privilege or remedy of any Subject Party (in any capacity) under the Escrow Agreement, nor shall the entering into of this Amendment preclude any Subject Party from refusing to enter into any further amendments with respect to the Escrow Agreement. Other than as otherwise expressly provided herein, this Amendment shall not constitute a waiver of compliance with any covenant or other provision in the Escrow Agreement or of the occurrence or continuance of any present or future Event of Default.

3.3 Ratification and Confirmation. Except as expressly set forth in this Amendment, the terms, provisions and conditions of the Escrow Agreement are hereby ratified and confirmed and shall remain unchanged and in full force and effect without interruption or impairment of any kind.

3.4 Choice of Law. The existence, validity, construction, operation and effect of any and all terms and provisions of this Amendment shall be determined in accordance with and governed by the laws of the State of New York, without regard to principles of conflicts of laws, except to the extent United States federal law is applicable to the perfection and priority of security interests in U.S. Government Securities.

3.5 Captions. Captions in this Amendment are for convenience only and shall not be considered or referred to in resolving questions of interpretation of this Amendment.

3.6 Counterparts. This Amendment may be executed in one or more counterparts, each of which shall be deemed an original but all of which together shall constitute one and the same instrument.

3.7 Invalidity. If for any reason whatsoever any one or more of the provisions of this Amendment shall be held or deemed to be inoperative, unenforceable or invalid in a particular case or in all cases, such circumstances shall not have the effect of rendering any of the other provisions of this Amendment inoperative, unenforceable or invalid, and the inoperative, unenforceable or invalid provision shall be construed as if it were written so as to effectuate, to the maximum extent possible, the parties’ intent.

3.8 Amendments. This Amendment may not be amended or modified except in the manner specified for an amendment of or modification to the Escrow Agreement in Section 8(f) of the Escrow Agreement.

3.9 Entire Agreement. This Amendment, the Escrow Agreement and the Indenture contain the entire agreement among the Subject Parties with respect to the subject matter hereof and supersede any and all prior agreements, understandings and commitments, whether oral or written.

3.10 Assignment. This Amendment is personal to the Subject Parties, and the rights and duties of any Subject Party hereunder shall not be assignable except as set forth in Section 2(e) of the Escrow Agreement or except as permitted by Section 5.1 of the Indenture, or, with respect to the Trustee, as allowed by the terms of the Indenture, or except with the prior written

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consent of the other Subject Parties. Notwithstanding the foregoing, this Amendment shall inure to and be binding upon the Subject Parties and their successors and permitted assigns.

3.11 Benefit. The Subject Parties and their successors and permitted assigns, but no others, shall be bound hereby and entitled to the benefits hereof; provided, however, that the Beneficiaries (including Holders) and their assigns shall be entitled to the benefits hereof and to enforce this Escrow Agreement.

[SIGNATURE PAGE FOLLOWS]

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IN WITNESS WHEREOF, the parties have executed this Amendment, or caused this Amendment to be executed by their authorized representatives, as of the date stated in the introductory paragraph of this Amendment.

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Amendment No. 1 to Escrow Agreement

Signature Page to

Amendment No. 1 to Escrow Agreement