EXHIBIT 10.73

                                 AMENDMENT NO. 1
                            TO SHAREHOLDERS AGREEMENT

     This  AMENDMENT  NO.  1  TO  SHAREHOLDERS  AGREEMENT  (the  "Amendment") is
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executed effective as of January 20, 1999, by and between Triton Energy Limited,
a Cayman Islands company (the "Company"), and HM4 Triton, L.P., a Cayman Islands
exempted  limited  partnership  (the  "Purchaser"),  to  amend  that  certain
Shareholders  Agreement,  dated  as  of  September  30,  1998 (the "Shareholders
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Agreement"),  by  and  between  the  Company  and  Purchaser.
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     1.     DEFINITIONS.  Unless  the  context  indicates otherwise, capitalized
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terms  used  but  not  defined in this Amendment and defined in the Shareholders
Agreement  shall  have  the meanings ascribed to them in the Purchase Agreement.

     2.     SECTION  4.1.7.  Section  4.1.7  is  hereby  amended  to read in its
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entirety  as  follow:

     4.1.7     Fees;  Costs  and  Expenses.  Except as provided in the following
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sentence, Holder Designees shall not receive an annual retainer, meeting fees or
other  consideration  for  serving  on  the Board (or committees thereof) or any
Board  of  Directors  of any Subsidiary of the Company.  The Company will pay or
reimburse  each  Holder  Designee  for  all  reasonable  out-of-pocket  expenses
incurred  by  such  Holder  Designee  in  connection  with  its participation in
meetings  of the Board (and committees thereof) and the Boards of Directors (and
committees  thereof)  of  the  Subsidiaries  of the Company. Notwithstanding the
foregoing,  any Holder Designee who is not an employee, principal or director of
the  Purchaser  or  Hicks,  Muse, Tate & Furst Incorporated shall be entitled to
receive  any annual retainer, meeting fees or other consideration for serving on
the Board (or committees thereof) or any Board of Directors of any Subsidiary of
the  Company  as  are provided to any director of the Company who is not also an
employee  of  the  Company  or  any  Subsidiary  of  the  Company.

     3.     REMAINING  PROVISIONS  IN FULL FORCE AND EFFECT.  As hereby amended,
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the  Purchase  Agreement  shall  remain  in  full  force  and  effect.


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     IN WITNESS WHEREOF, each of the parties hereto has caused this Amendment to
be  executed  by  its  duly authorized officer effective as of January 20, 1999.

                    TRITON  ENERGY  LIMITED



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


                    HM4  TRITON,  L.P.

                    By:  HM4/GP  Partners  Cayman,  L.P.,
                         its  General  Partner

                         By:  HM  GP  Partners  IV  Cayman,  L.P.,
                              its  General  Partner


                              By:  HM Triton G.P., LLC,
                                   its General Partner


                                   By:____________________
                                      Daniel  S.  Dross
                                      Senior  Vice  President