TRITON ENERGY LIMITED
                           CALEDONIAN HOUSE, MARY STREET
                                   P.O. BOX 1043
                                    GEORGE TOWN
                            GRAND CAYMAN, CAYMAN ISLANDS

Dear Shareholder:

     This letter is sent to remind shareholders of Triton Energy Limited that
the Annual Meeting of Shareholders will be held at 10:00 a.m., Dallas time, on
Tuesday, May 12, 1998, at the Royal Oaks Country Club, 7915 Greenville Avenue,
Dallas, Texas 75231. The Company encourages all persons who were shareholders as
of March 27, 1998 to mark, date, sign and return the proxy card that was
enclosed with the Proxy Statement dated April 2, 1998.

     This letter also supplements the Proxy Statement by noting that the table
heading "Class II - Term Expiring 2000" above the four nominees for three year
terms (Messrs. Hudson, Huff, Musselman and Norsworthy) under the table of
nominees on page 4 of the Proxy Statement should instead be "Class III - Term
Expiring 2001."


                                       Sincerely,


                                       Robert B. Holland, III
                                       SECRETARY

April 17, 1998