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                                                                   EXHIBIT 10.85


                               SECOND AMENDMENT TO
                AMENDED AND RESTATED 1997 SHARE COMPENSATION PLAN

         This Second Amendment to the Amended and Restated 1997 Share
Compensation Plan (this "Amendment") is executed by Triton Energy Limited, a
Cayman Islands company ("Triton"), effective as of January 3, 2000.

                                    RECITALS:

         A. Triton has adopted the Amended and Restated 1997 Share Compensation
Plan (the "Plan") effective as of December 2, 1998; and

         B. In accordance with the terms of the Plan, the Compensation Committee
of the Board of Directors has adopted certain amendments to the Plan effective
as of January 10, 2000.

         NOW, THEREFORE, in accordance with the terms of the Plan, the Plan is
amended in the following respects:

         1. Section 5.7(a) of the Plan is hereby amended to read in its entirety
as set forth below:

            "(a) Grant of Stock Options. In addition to the options provided for
         in this Article V, throughout the term of this Plan, on the first
         business day of January of each year (or if such day is not business
         day, then the next succeeding business day) each Non-Employee Director
         of the Company shall automatically receive a Nonqualified Stock Option
         to purchase 15,000 Ordinary Shares. In addition, upon a person being
         first appointed or elected as a Non-Employee Director, such person
         shall automatically receive a Nonqualified Stock Option to purchase
         15,000 Ordinary Shares. Notwithstanding anything in the foregoing to
         the contrary, in no event shall any Holder Designee (as defined in that
         certain Shareholders Agreement dated as of September 30, 1998, between
         the Company and HM4 Triton, L.P.) who is an employee, principal or
         director of HM4 Triton, L.P. or Hicks, Muse, Tate & Furst Incorporated
         be entitled to receive Stock Options pursuant to this Section 5.7(a),
         whether on an annual basis or upon his or her first appointment or
         election as a Non-Employee Director."

         2. Except as amended by the provisions of this Amendment, all other
provisions of the Plan remain in full force and effect.

         IN WITNESS WHEREOF, Triton has caused this Amendment to be executed by
its duly authorized officer effective as of the date and year first above
written.

                                       TRITON ENERGY LIMITED



                                       By:
                                          --------------------------------------
                                            James C. Musselman, President and
                                            Chief Executive Officer