<PAGE>   1


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                     FIRST AMENDMENT TO CREDIT AGREEMENT



                                    AMONG


                           PRIMEENERGY CORPORATION
                                     AND

                     PRIMEENERGY MANAGEMENT CORPORATION,
                                AS BORROWERS,
                    BANK ONE, TEXAS, NATIONAL ASSOCIATION,
                                  AS AGENT,

                                     AND

                         THE LENDERS SIGNATORY HERETO


                       Effective as of October 6, 1995


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<PAGE>   2

                               TABLE OF CONTENTS

<TABLE>
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<S>              <C>                                                                                                    <C>
ARTICLE I        DEFINITIONS AND INTERPRETATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         1.01    Terms Defined Above  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         1.02    Terms Defined in Credit Agreement  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         1.03    References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         1.04    Articles and Sections  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
         1.05    Number and Gender  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

ARTICLE II       AMENDMENTS TO CREDIT AGREEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
         2.01    Amendment of Section 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
         2.02    Amendment of Section 6.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

ARTICLE III      CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         3.01    Receipt of Loan Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         3.02    Accuracy of Representations and Warranties; No Default or Event of Default . . . . . . . . . . . . . . 3
         3.03    Payment of Fees and Expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         3.04    Matters Satisfactory to Lenders  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         3.05    No Material Adverse Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

ARTICLE IV       REPRESENTATIONS AND WARRANTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         4.01    Due Authorization  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         4.02    Valid and Binding Obligations of Borrowers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         4.03    Representations and Warranties in Credit Agreement . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         4.04    No Default or Event of Default . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         4.05    Ratification and Confirmation of Liens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

ARTICLE V        MISCELLANEOUS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         5.01    Survival Upon Unenforceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         5.02    Rights of Third Parties  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         5.03    Amendments or Modifications  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         5.04    Ratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         5.05    Expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         5.06    ENTIRE AGREEMENT; NO ORAL AGREEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         5.07    GOVERNING LAW  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         5.08    JURISDICTION AND VENUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         5.09    Counterparts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

</TABLE>




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                      FIRST AMENDMENT TO CREDIT AGREEMENT


                 THIS FIRST AMENDMENT TO CREDIT AGREEMENT (this "Amendment"),
effective as of October 6, 1995, is entered into by and among PRIMEENERGY
CORPORATION, a Delaware corporation ("PEC"), PRIMEENERGY MANAGEMENT
CORPORATION, a New York corporation ("PEMC," with PEC and PEMC being
individually referred to as a "Borrower" and collectively as the "Borrowers"),
BANK ONE, TEXAS, N.A., a national banking association ("Bank One"), and DEN
NORSKE BANK AS, a Norwegian bank ("DNB," with Bank One, DNB, and each other
lender that becomes signatory, individually, together with its successors and
assigns, a "Lender" and, collectively, together with their respective successors
and assigns, the "Lenders"), and Bank One, as agent for the Lenders (in such
capacity, together with its successors in such capacity, the "Agent").

                                  WITNESSETH:

                 WHEREAS, the Borrowers and the Lenders are parties to the
Credit Agreement dated as of April 26, 1995 (the "Credit Agreement"); and

                 WHEREAS, the Borrowers and the Lenders desire to amend the
Credit Agreement as provided hereinbelow;

                 NOW THEREFORE, in consideration of the premises and the mutual
agreements, representations and warranties herein set forth and for other good
and valuable consideration, the Borrowers and the Lenders hereby agree as
follows:


                                   ARTICLE I

                         DEFINITIONS AND INTERPRETATION

                 1.01     Terms Defined Above. As used in this Amendment, each
of the terms "Agent," "Amendment," "Bank One," "Borrower," "Borrowers," 
"Credit Agreement," "DNB," "Lender," "Lenders," "PEC," and "PEMC" shall have
the meaning assigned to such term hereinabove.

                 1.02     Terms Defined in Credit Agreement. Each term defined
in the Credit Agreement and used herein without definition shall have the
meaning assigned to such term in the Credit Agreement, unless expressly
provided herein to the contrary.

                 1.03     References. References in this Amendment to Article
or Section numbers shall be to Articles and Sections of this Amendment, unless
expressly stated herein to the contrary. References in this Amendment to
"hereby," "herein," "hereinabove," "hereinafter," "hereinbelow," "hereof," and
"hereunder" shall be to this Amendment in its entirety and not only to the
particular Article or Section in which such reference appears.
<PAGE>   4
                 1.04     Articles and Sections. This Amendment, for
convenience only, has been divided into Articles and Sections, and all rights,
powers, privileges, duties, and other legal relations of the parties hereto
shall be determined from this Amendment as an entirety and without regard to
such divisions into Articles and Sections and without regard to headings
prefixed to such Articles and Sections.

                 1.05     Number and Gender. Whenever the context requires,
reference herein made to the single number shall be understood to include the
plural and likewise the plural shall be understood to include the singular.
Words denoting sex shall be construed to include the masculine, feminine, and
neuter, when such construction is appropriate; and specific enumeration shall
not exclude the general but shall be construed as cumulative. Definitions of
terms defined in the singular and plural shall be equally applicable to the
plural and singular, as the case may be.


                                   ARTICLE II

                         AMENDMENTS TO CREDIT AGREEMENT

                 2.01     Amendment of Section 1.2. The following definitions
set forth in Section 1.2 of the Credit Agreement are hereby amended to read as
follows:

                 "'Commitment Termination Date' shall mean July 1, 1998."

                 "'Final Maturity' shall mean July 1, 1998."

                 2.02     Amendment of Section 6.8. Section 6.8 of the Credit
Agreement is hereby amended to read in its entirety as follows:

                 "6.8 Dividends and Distributions. Declare, pay, or make,
         whether in cash or other Property, any dividend or distribution on any
         share of any class of the capital stock of either Borrower, or
         purchase, redeem, or otherwise acquire for value any share of any
         class of capital stock of either Borrower other than the purchase by
         PEC of the capital stock of PEC for an amount not exceeding $1,250,000
         in any fiscal year provided that no Default or Event of Default exists
         or will occur as the result of such purchase and provided further that
         the Lender has received written notice of any such purchase for an
         amount exceeding $100,000."


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                                  ARTICLE III

                                   CONDITIONS

                 The obligation of the Agent and the Lenders to amend the
Credit Agreement as provided herein is subject to the fulfillment of the
following conditions president:

                 3.01     Receipt of Loan Documents. The Agent shall have
received multiple counterparts, as requested by the Agent, of this Amendment,
executed by the Borrowers, which shall be in form and substance satisfactory to
the Agent.

                 3.02     Accuracy of Representations and Warranties: No
Default or Event of Default. The representations and warranties contained in
Article IV of this Amendment shall be true and correct in all material
respects; and no Default or Event of Default shall have occurred and be
continuing.

                 3.03     Payment of Fees and Expenses. The Agent shall have
received reimbursement from the Borrowers, or special legal counsel for the
Agent shall have received payment from the Borrowers, for all reasonable fees
and expenses of counsel to the Lenders for which the Borrowers are responsible
pursuant to applicable provisions of this Amendment and the Credit Agreement
for which invoices have been presented as of or prior to the date hereof.

                 3.04     Matters Satisfactory to Lenders. All matters incident
to the consummation of the transactions hereby contemplated shall be reasonably
satisfactory to the Lenders.

                 3.05     No Material Adverse Effect. No event or circumstance
shall have occurred since June 30, 1995, that could reasonably be expected to
have a Material Adverse Effect.


                                   ARTICLE IV

                         REPRESENTATIONS AND WARRANTIES

                 To induce the Agent and the Lenders to enter into this
Amendment and amend the Credit Agreement as provided herein, the Borrowers
represent and warrant to the Agent and each Lender that:

                 4.01     Due Authorization. The execution and delivery by the
Borrowers of this Amendment and the performance of its obligations hereunder
are within the power of the Borrowers, are duly authorized by all necessary
action on behalf of the Borrowers, and do not and will not (a) require the
consent of any Governmental Authority, (b) contravene or conflict with any
Requirement of Law or the articles or certificate of incorporation, bylaws, or
other organizational or governing documents of the Borrowers, (c) contravene or
conflict with any indenture, instrument or other agreement to which either
Borrower is a party or by which its Property may be presently bound or
encumbered, or (d) result in or require the creation or




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imposition of any Lien upon any of the properties or assets of either Borrower
under any such indenture, instrument or other agreement other than the Loan
Documents.

                 4.02     Valid and Binding Obligations of Borrowers. This
Amendment, when duly executed and delivered, will be the legal, valid and
binding obligation of the Borrowers, enforceable in accordance with its terms
(subject to any applicable bankruptcy, insolvency or other laws of general
application affecting creditors' rights and judicial decisions interpreting any
of the foregoing).

                 4.03     Representations and Warranties in Credit Agreement.
As of the date hereof, all representations and warranties set forth in the
Credit Agreement are true and correct in all material respects, except to the
extent such representations and warranties relate solely to an earlier date.

                 4.04     No Default or Event of Default. No Default or Event 
of Default exists.

                 4.05     Ratification and Confirmation of Liens. The Borrowers
hereby ratify and confirm all Liens created under the Security Instruments and
acknowledge and agree that all such Liens secure all Obligations.


                                   ARTICLE V

                                 MISCELLANEOUS

                 5.01     Survival Upon Unenforceability. In the event any one
or more of the provisions contained in this Amendment shall, for any reason, be
held to be invalid, illegal or unenforceable in any respect, such invalidity,
illegality, or unenforceability shall not affect any other provision hereof.

                 5.02     Rights of Third Parties. All provisions herein are
imposed solely and exclusively for the benefit of the Agent, the Lenders and
the Borrowers, and their successors and permitted assigns. No other Person
shall have any right, benefit, priority, or interest hereunder or as a result
hereof or have standing to require satisfaction of provisions hereof in
accordance with their terms.

                 5.03     Amendments or Modifications. Neither this Amendment
nor any provision hereof may be changed, waived, discharged or terminated
orally, but only by an instrument in writing signed by the party against whom
enforcement of the change, waiver, discharge or termination is sought.

                 5.04     Ratification. Except as expressly amended by this
Amendment and the documents executed in connection herewith, the Credit
Agreement and all other Loan Documents shall remain in full force and effect.
The Credit Agreement, as hereby amended, and all rights




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<PAGE>   7
and powers created thereby or thereunder and under such other Loan Documents
are in all respects ratified and confirmed.

                  5.05    Expenses. The Borrowers shall pay to the Agent for
the benefit of the Lenders promptly upon request all expenses incurred in
connection with this Amendment and the documents executed in connection
herewith.

                 5.06      ENTIRE AGREEMENT; NO ORAL AGREEMENTS. THIS AGREEMENT
CONSTITUTES THE ENTIRE AGREEMENT OF THE PARTIES HERETO WITH RESPECT TO THE 
SUBJECT HEREOF AND SUPERSEDES ANY PRIOR AGREEMENT BETWEEN THE PARTIES HERETO,
WHETHER WRITTEN OR ORAL, RELATING TO THE SUBJECT HEREOF. THIS WRITTEN AGREEMENT
AND THE OTHER WRITTEN LOAN DOCUMENTS REPRESENT, COLLECTIVELY, THE FINAL
AGREEMENT AMONG THE PARTIES HERETO AND THERETO AND MAY NOT BE CONTRADICTED BY
EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE
PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS AMONG THE PARTIES.

                 5.07     GOVERNING LAW. THIS AMENDMENT SHALL BE GOVERNED BY
AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS (WITHOUT GIVING
EFFECT TO PRINCIPLES THEREOF RELATING TO CONFLICTS OF LAW); PROVIDED, HOWEVER,
THAT VERNON'S TEXAS CIVIL STATUTES, ARTICLE 5069, CHAPTER 15 (WHICH REGULATES
CERTAIN REVOLVING CREDIT LOAN ACCOUNTS AND REVOLVING TRIPARTY ACCOUNTS) SHALL
NOT APPLY.

                  5.08     JURISDICTION AND VENUE. ALL ACTIONS OR PROCEEDINGS
WITH RESPECT TO, ARISING DIRECTLY OR INDIRECTLY IN CONNECTION WITH, OUT OF,
RELATED TO OR FROM THIS AMENDMENT MAY BE LITIGATED, AT THE SOLE DISCRETION AND
ELECTION OF THE AGENT, IN COURTS HAVING SITUS IN HOUSTON, HARRIS COUNTY, TEXAS.
EACH BORROWER HEREBY SUBMITS TO THE JURISDICTION OF ANY LOCAL, STATE OR FEDERAL
COURT LOCATED IN HOUSTON, HARRIS COUNTY, TEXAS, AND HEREBY WAIVES ANY RIGHTS IT
MAY HAVE TO TRANSFER OR CHANGE THE JURISDICTION OR VENUE OF ANY LITIGATION
BROUGHT AGAINST IT BY THE AGENT IN ACCORDANCE WITH THIS SECTION.

                  5.09    Counterparts. This Amendment may be signed in any
number of counterparts and by different parties in separate counterparts, each
of which shall be deemed an original but all of which together shall constitute
one and the same instrument.




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<PAGE>   8

          IN WITNESS WHEREOF, the parties have caused this Amendment to be
executed by their respective duly authorized officers on the date first
hereinabove written.

                                        BORROWER:

                                        PRIMEENERGY CORPORATION


                                        By:  /s/ BEVERLY A. CUMMINGS
                                            ----------------------------------
                                            Beverly A. Cummings
                                            Executive Vice President, Treasurer
                                            and Chief Financial Officer
                                        
                                         

                                        BORROWER:

                                        PRIMEENERGY MANAGEMENT
                                        CORPORATION


                                        By:  /s/ BEVERLY A. CUMMINGS
                                            ----------------------------------
                                            Beverly A. Cummings
                                            Executive Vice President, Treasurer
                                            and Chief Financial Officer


                                        AGENT AND LENDER:

                                        BANK ONE, TEXAS, NATIONAL
                                        ASSOCIATION

                                        By:  /s/ KELLY L. ELMORE, III
                                            ----------------------------------
                                            Kelly L. Elmore, III
                                            Vice President
                                        





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                                        LENDER

                                        DEN NORSKE BANK AS 


                                        By: /s/ THEODORE S. JADICK, JR.
                                           ----------------------------------
                                        Name:   Theodore S. Jadick, Jr.
                                              -------------------------------
                                        Title: Senior Vice President
                                              -------------------------------


                                        By: /s/ FRAN MEYERS
                                           ----------------------------------
                                        Name:   Fran Meyers
                                              -------------------------------
                                        Title:  Vice President
                                              -------------------------------



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