EXHIBIT 10.73

                               SECOND AMENDMENT TO
                               -------------------
                          1997 SHARE COMPENSATION PLAN
                          ----------------------------

     This  Second  Amendment  to  the  1997  Share  Compensation  Plan  (this
"Amendment")  is  executed  by  Triton  Energy Limited, a Cayman Islands company
("Triton"),  as  of  September  28,  1998.

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

     A.     Triton has adopted the 1997 Share Compensation Plan (as amended, the
"Plan");  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.     Article  III  is  amended  to  read  in  its  entirety  as  follows:

"The Committee may not grant Stock Options or issue Elected Shares or Restricted
Shares  under the Plan for more than 2,300,000 Ordinary Shares, in the aggregate
(as  may  be  adjusted  in  accordance  with  Article  XI or XII hereof), and no
Participant  shall  be eligible to receive more than 50% of such shares.  Shares
to  be  distributed  and  sold  may be made available from either authorized but
unissued Ordinary Shares or Ordinary Shares held by the Company in its treasury.
Shares  that  by  reason of the expiration or unexercised termination of a Stock
Option or forfeited Elected Shares or Restricted Shares are no longer subject to
issuance  to  the  Participant  may  be  reofferred  under  the  Plan."

     2.     Section  4.2  is  amended  to  read  in  its  entirety  as  follows:

     4.2     Election  to  Receive  Elected  Shares  and/or Stock Options.  Each
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Participant  eligible to receive Elected Shares may make an irrevocable election
(an  "Election")  either  (a)  to receive a grant of Ordinary Shares in a number
determined by the Committee from time to time in an amount or amounts determined
by  the  Committee  (whether  in  a  fixed  amount  or by formula) or (b) not to
participate  in  this  Article  IV.  With  respect  to  the  participation  by
Non-Employee Directors, each such Director is automatically eligible to elect to
receive  a  grant  of  1,000  Elected  Shares in conjunction with an election to
receive  a grant of Stock Options to purchase 10,000 Ordinary Shares pursuant to
Section  5.7  of  the  Plan,  except  as  provided  in  Section 5.7 of the Plan.

     3.     Section 5.7(a) of the Plan is amended by adding as the last sentence
to  Section  5.7(a)  the  following:

"Notwithstanding  anything  in  the foregoing to the contrary, in no event shall
any  Holder  Designee (as defined in that certain Shareholders Agreement entered
into,  or  to be entered into, between the Company and HM4 Triton, L.P. pursuant
to that certain Stock Purchase Agreement dated as of August 31, 1998 between the
Company  and  HM4  Triton,  L.P.) be entitled to elect to receive Elected Shares
pursuant  to  Section  4.2 of the Plan or 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."

     4.     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 Energy Limited 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:/s/ Robert B. Holland, III
                                 ---------------------------------------
                                 Robert B. Holland, III, Chief Executive
                                 Officer