<PAGE>   1
                                                                 EXHIBIT 10.7.2

===============================================================================

                     SECOND 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 February 6, 1997

===============================================================================

<PAGE>   2


                               TABLE OF CONTENTS
<TABLE>
<CAPTION>

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

ARTICLE II    AMENDMENTS ...................................................   2
              2.01 Amendment of Section 1.2 ................................   2
              2.02 Amendment of Section 2.11(b) ............................   2
              2.03 Amendment of Section 2.16 ...............................   3

ARTICLE III   CONDITIONS ...................................................   3
              3.01 Receipt of Loan Documents ...............................   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 ...............................   4
              4.01 Due Authorization .......................................   4
              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 ................................................   5
              5.01 Survival Upon Unenforceability ..........................   5
              5.02 Rights of Third Parties .................................   5
              5.03 Amendments or Modifications .............................   5
              5.04 Ratification ............................................   5
              5.05 Expenses ................................................   5
              5.06 ENTIRE AGREEMENT; NO ORAL AGREEMENTS ....................   5
              5.07 GOVERNING LAW ...........................................   5
              5.08 JURISDICTION AND VENUE ..................................   6
              5.09 Counterparts ............................................   6
</TABLE>



                                       i
<PAGE>   3


                      SECOND AMENDMENT TO CREDIT AGREEMENT


      This SECOND AGREEMENT TO CREDIT AGREEMENT (this "Second Amendment") is
made and entered into effective as of February 6, 1997, 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, NATIONAL ASSOCIATION, 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 above named parties did execute and exchange counterparts of
that certain Credit Agreement dated April 26, 1995, as amended by First
Amendment to Credit Agreement dated effective as of October 6, 1995 (the
"Agreement"), to which reference is here made for all purposes;

      WHEREAS, the parties subject to and bound by the Agreement are desirous
of amending the Agreement in the particulars hereinafter set forth;

      NOW, THEREFORE, in consideration of the mutual covenants and agreements
of the parties to the Agreement, as set forth therein, and the mutual covenants
and agreements of the parties hereto, as set forth in this Second Amendment,
the parties hereto agree as follows:


                                   ARTICLE I

                                  DEFINITIONS

      1.01 Terms Defined Above. As used herein, each of the terms "Agent,"
"Second 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 Agreement. As used herein, each term defined in the
Agreement shall have the meaning assigned thereto in the Agreement, unless
expressly provided herein to the contrary.

      1.03 References. References in this Second Amendment to Article or
Section numbers shall be to Articles and Sections of this Second Amendment,
unless expressly stated herein to the contrary. References in this Second
Amendment to "hereby," "herein,"


<PAGE>   4


"hereinafter," "hereinabove," "hereinbelow," "hereof," and "hereunder" shall be
to this Second Amendment in its entirety and not only to the particular Article
or Section in which such reference appears.

      1.04 Articles and Sections. This Second Amendment, for convenience only,
has been divided into Articles and Sections and it is understood that the
rights, powers, privileges, duties, and other legal relations of the parties
hereto shall be determined from this Second Amendment as an entirety and
without regard to such division 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 or
singular, as the case may be.


                                   ARTICLE II

                                   AMENDMENTS

      The Borrower and the Lender hereby amend the Agreement in the following
particulars:

      2.01 Amendment of Section 1.2. Section 1.2 of the Agreement is hereby
amended as follows:

      The following definitions are added or amended to read as follows:

      "'Commitment Termination Date' shall mean July 1, 2000."

      "'Final Maturity' shall mean July 1, 2000. "

      "'Applicable Margin' shall mean, as to each Floating Rate Loan, zero
      percent (O%), and as to each LIBO Rate Loan, two and one-quarter percent
      (2 1/4%), which shall include any LIBO Rate Loans maturing subsequent to
      February 6, 1997."

      2.02 Amendment of Section 2.11 (b). The first two sentences of Section
2.11(b) are amended as follows:

      "The Borrowing Base as of February 6, 1997, is acknowledged by the
      Borrowers and the Lender to be $21,000,000. The Reserve



                                       2
<PAGE>   5


      Value as of February 6, 1997, is acknowledged by the Borrowers and the
      Lender to be $9,175,000."

      2.03 Amendment of Section 2.16. Section 2.16 is amended to add the
following:

      "... The Borrower shall not be required to pay a facility fee on February
      6, 1997, and such fee, if any, will be paid if the Borrowing Base as
      determined on July 1, 1997, is in excess of $19,250,000 and the facility
      fee will be one percent (1 %) of the excess over such sum."


                                  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
precedent:

      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.



                                       3
<PAGE>   6


                                   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 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.



                                       4
<PAGE>   7


                                   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 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 AMENDMENT 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



                                       5
<PAGE>   8


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.

      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:
                                                 -----------------------------
                                                    Beverly A. Cummings
                                                    Executive Vice President,
                                                    Treasurer and
                                                    Chief Financial Officer


                                              BORROWER:

                                              PRIMEENERGY MANAGEMENT
                                              CORPORATION


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




                                       6
<PAGE>   9


                                               AGENT AND LENDER:

                                               BANK ONE, TEXAS, NATIONAL
                                               ASSOCIATION


                                               By:
                                                 -------------------------------
                                                   Kelly L. Elmore, III
                                                   Vice President



                                               LENDER:

                                               DEN NORSKE BANK AS


                                               By:
                                                 -------------------------------
                                                 William V. Moyer
                                                 Vice President


                                               By:
                                                  ------------------------------
                                               Name:
                                                    ----------------------------
                                               Title:
                                                     ---------------------------





                                       7