EXHIBIT 10.68


                               THIRD AMENDMENT TO
                               ------------------
                AMENDED AND RESTATED 1997 SHARE COMPENSATION PLAN
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     This  Third  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  May  16,  2001.

                                R E C I T A L S:
                                ---------------

     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 Board of Directors has
adopted  certain  amendments  to  the  Plan.

     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 by adding the following
sentence  to  the  end  of  such  Section:

     "Notwithstanding  anything  in the foregoing, or any other provision of the
Plan,  to  the  contrary, from and after May 16, 2001, there shall be no further
grants  of  Stock  Options  under  this  Section  5.7."


     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