<PAGE>
 
                                                                   EXHIBIT 10(d)

                             FIRST AMENDMENT TO THE
                                 AMAX GOLD INC.
                     KEY EXECUTIVE LONG-TERM INCENTIVE PLAN


     This First Amendment to the AMAX GOLD INC. ("Company") KEY EXECUTIVE LONG-
TERM INCENTIVE PLAN (the "Plan") is effective the 1st day of December, 1996.

                                    Recitals

A.   The Plan has been in effect since January 1, 1993 and permits the award of
equity-based incentive compensation.

B.   The amendment made herein has been approved by the Company's Board of
Directors on the 11th day of December, 1996.

                                   Amendments

1.   Section 1.1(s) is hereby amended and restated in its entirety as follows:

     "Plan" shall mean this Amax Gold Inc. Key Executive Long-Term Incentive
     Plan.

Executed at Arapahoe County, Colorado this 31st day of March, 1997.


                                    AMAX GOLD INC.



                                    By:   /s/ S. SCOTT SHELLHAAS
                                       --------------------------------
                                          S. Scott Shellhaas
                                          President and Chief
                                          Operating Officer
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                                                                   EXHIBIT 10(d)

                            SECOND AMENDMENT TO THE
                                 AMAX GOLD INC.
                     KEY EXECUTIVE LONG-TERM INCENTIVE PLAN


     This Second Amendment to the AMAX GOLD INC. ("Company") KEY EXECUTIVE LONG-
TERM INCENTIVE PLAN (the "Plan") is effective the 1st day of December, 1996.

                                    Recitals

A.   The Plan has been in effect since January 1, 1993, and permits the award of
equity-based incentive compensation.

B.   In 1996, the Securities and Exchange Commission amended the provisions of
Rule 16b-3 of Section 16(b) of the Securities Exchange Act of 1934, and the
Company desires to amend the Plan to conform to certain changes made in Rule
16b-3.

C.   On December 11, 1996, the Compensation Committee of the Company's Board of
Directors authorized a change in the name of the Plan.

D.   The amendment made herein has been approved by the Company's Board of
Directors on the 12th day of February, 1997.

                                   Amendments

1.   Section 1.1(i) of the Plan is hereby amended in its entirety to read as
     follows:

          (i) "Compensation Committee" shall mean the Compensation Committee of
     the Board of Directors, a standing committee of not fewer than two Non-
     Employee Directors (as such term is defined under Rule 16a of the Exchange
     Act), who shall administer and interpret the Plan.

Executed at Arapahoe County, Colorado this 31st day of March, 1997.

                                    AMAX GOLD INC.



                                    By:   /s/ S. SCOTT SHELLHAAS
                                       -------------------------------------
                                          S. Scott Shellhaas
                                          President and Chief
                                          Operating Officer