<PAGE>   1
                                                                   EXHIBIT 10(a)



                                        April 1, 1997


NYLIFE Inc.
51 Madison Avenue
New York, New York 10010

Dear Sirs:

                 This letter agreement shall serve as an amendment (the
"Amendment") to the Agreement dated February 15, 1996, by and among American
Exploration Company, American Exploration Production Company, and NYLIFE Inc.,
(the "Agreement").  Defined terms used herein have the meaning attributed to
them in the Agreement.

                 The existing language in Paragraph 7 of the Agreement shall be
deleted in its entirety and replaced with the following:

                          Agreement in Lieu of Liquidation Reserve

                          In lieu of the establishment by any NYLOG
                          Partnership, or the general partners thereof, of any
                          reserve for contingent liabilities in connection with
                          any dissolution and liquidation of the NYLOG
                          Partnerships, as contemplated by this Agreement,
                          NYLIFE and the American Parties agree as follows:
<PAGE>   2
                          Upon the payment by NYLIFE of $2.5 million to AX
                          concurrently with liquidation of the NYLOG
                          Partnerships, all Liabilities, as hereinafter
                          defined, of the NYLOG Partnerships, will be borne (i)
                          up to an aggregate amount of $2.5 million by the
                          American Parties, (ii) in excess of $2.5 million
                          through $4.0 million by NYLIFE, and (iii) in excess
                          of $4.0 million through $8.0 million by the American
                          Parties.  All Liabilities in excess of $8 million
                          will be borne equally by the American Parties on the
                          one hand and NYLIFE on the other.  For purposes of
                          this Agreement, the term "Liabilities" shall include
                          all amounts, including, but not limited to, third
                          party costs, expenses, fees, disbursements (including
                          counsels' fees and disbursements), judgments,
                          payments in settlement and other amounts paid or due,
                          which could be reserved for in connection with the
                          dissolution and liquidation of the NYLOG
                          Partnerships, but excluding (i) all internal costs of
                          AX, AEPCO and their affiliates that would otherwise
                          be classified as Liabilities, (ii) all Indemnified
                          Liabilities and rights with respect thereto of the
                          American Indemnified Parties and (iii) specific
                          liabilities assumed pursuant to the letter agreement,
                          dated April 2, 1997, among the American Parties and
                          NYLIFE Equity Inc.

All other terms and provisions of the Agreement shall remain in full force and
effect.


                                      2
<PAGE>   3
                 If the foregoing is satisfactory, please indicate your consent
to, and agreement with, the Amendment by signing the enclosed copy hereof and
returning the same to the undersigned, whereupon this letter shall become a
binding agreement among the parties hereto.


                                        AMERICAN EXPLORATION COMPANY
                                        and AMERICAN EXPLORATION
                                           PRODUCTION COMPANY
                        
                        
                        
                                        By: /s/ JOHN M. HOGAN                 
                                            ----------------------------------
                                                 Name:  John M. Hogan
                                                 Title:    Sr. V.P. & CFO
                        
                        
CONSENTED AND AGREED TO
as of the 1st day of April, 1997

NYLIFE INC.



By: /s/ ALICE T. KANE            
    -----------------------------
        Name:  Alice T. Kane
        Title: Vice President



                                      3