TRITON ENERGY CORP
SC 13G/A, 1998-04-06
CRUDE PETROLEUM & NATURAL GAS
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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549



                                  SCHEDULE 13G

INFORMATION STATEMENT PURSUANT TO RULES 13d-1(b) AND (c) AND AMENDMENTS THERETO
FILED PURSUANT TO 13d-2(b)

                               (AMENDMENT NO. 1)*


                            TRITON ENERGY CORPORATION
                            -------------------------
                                (Name of Issuer)


                                  COMMON STOCK
                         ------------------------------
                         (Title of Class of Securities)


                                    G90751101
                                 --------------
                                 (CUSIP Number)










        *The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class of
securities, and for any subsequent amendment containing information which would
alter the disclosures provided in a prior cover page.

        The information required in the remainder of this cover page shall not
be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
the Act but shall be subject to all other provisions of the Act (however, see
the Notes).


<PAGE>   2


CUSIP NO. G90751101                     13G            PAGE   2   OF   5   PAGES
         ---------------------                              -----    -----      

  (1)     NAME OF REPORTING PERSON
          S.S. OR I.R.S. IDENTIFICATION OF ABOVE PERSON               

          OPPENHEIMER CAPITAL (IRS NO. 13-3413767)
          ---------------------------------------------------------------------

  (2)     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*         (a)   [   ]
                                                                    (b)   [ X ]

          --------------------------------------------------------------------- 

  (3)     SEC USE ONLY

          ---------------------------------------------------------------------

  (4)     CITIZENSHIP OR PLACE OF ORGANIZATION                      

          DELAWARE
          ---------------------------------------------------------------------

                       (5)     SOLE VOTING POWER                    
  NUMBER OF                    -0-
   SHARES              --------------------------------------------------------
 BENEFICIALLY          (6)     SHARED VOTING POWER                  
  OWNED BY                     3,156,846
    EACH               --------------------------------------------------------
  REPORTING            (7)     SOLE DISPOSITIVE POWER               
 PERSON WITH                   -0-
                       --------------------------------------------------------
                       (8)     SHARED DISPOSITIVE POWER             

                               3,156,846
                       --------------------------------------------------------

  (9)     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON         
          
          3,156,846
          ---------------------------------------------------------------------

 (10)     CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
          SHARES*                                                         [   ]

          ---------------------------------------------------------------------

 (11)     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)           

          8.63
          ---------------------------------------------------------------------

 (12)     TYPE OF REPORTING PERSON*

          IA
          ---------------------------------------------------------------------
                    *SEE INSTRUCTIONS BEFORE FILLING OUT!



                                       2
<PAGE>   3




ITEM 1  (a)    NAME OF ISSUER: Triton Energy Corporation

        (b)    ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:
               6688 North Central Expressway, Suite 1400
               Dallas, TX 75204

ITEM 2  (a)    NAME OF PERSON FILING: OPPENHEIMER CAPITAL

        (b)    ADDRESS OF PRINCIPAL BUSINESS OFFICE:
               Oppenheimer Tower, World Financial Center 
               New York, New York 10281

        (c)    CITIZENSHIP:
               Not Applicable.

        (d)    TITLE OF CLASS OF SECURITIES:
               Common Stock

        (e)    CUSIP NUMBER:
               G90751101

ITEM 3  IF THIS STATEMENT IS FILED PURSUANT TO RULE 13D-1(B), OR 13D-2(B), CHECK
        WHETHER THE PERSON FILING IS A:

               (a)  [ ] Broker or Dealer registered under Section 15 of the
                        Act.

               (b)  [ ] Bank as defined in Section 3(a)(6) of the Act.

               (c)  [ ] Insurance Company as defined in Section 3(a)(19) of the
                        Act.

               (d)  [ ] Investment Company registered under Section 8 of the
                        Investment Company Act.

               (e)  [X] Investment Adviser registered under Section 203 of the
                        Investment Advisors Act of 1940.

               (f)  [ ] Employee Benefit Plan, Pension Fund which is subject to
                        the provisions of the Employee Retirement Income
                        Security Act of 1974 or Endowment Fund; see
                        Paragraph 240.13d-1(b)(1)(ii)(F).

               (g)  [ ] Parent Holding Company, in accordance with
                        Paragraph 13d-1(b)(ii)(G).

               (h)  [ ] Group, in accordance with Paragraph 13d-1(b)(1)(ii)(H).




                                       3
<PAGE>   4



ITEM 4  OWNERSHIP.

        (a)    Amount beneficially owned: 3,156,846 **

        (b)    Percent of Class: 8.63

        (c)    Number of shares as to which such person has:

        (i)    Sole power to vote or direct the vote: -0-

        (ii)   Shared power to vote: 3,156,846 **

        (iii)  Sole power to dispose or direct the disposition of: -0-

        (iv)   Shared power to dispose or direct the disposition of: 
               3,156,846 **

        **This report is being filed on behalf of Oppenheimer Capital, a
Delaware general partnership and/or certain investment advisory clients or
discretionary accounts relating to their collective beneficial ownership of
shares of common stock of the Issuer. Oppenheimer Capital is a registered
investment adviser under Section 203 of the Investment Advisers Act of 1940. As
a result of its role as investment adviser Oppenheimer may be deemed to be the
beneficial owner of the securities of the Issuer. Oppenheimer Capital has the
sole power to dispose of the shares and to vote the shares under its written
guidelines established by its Management Board.

ITEM 5  OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS.

        If this statement is being filed to report the fact that as of the date
hereof the reporting person has ceased to be the beneficial owner of more than
five percent of the class of securities, check the following [ ].

ITEM 6  OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON.

        Our clients have the right to receive or the power to direct the receipt
of dividends or the profits from the sale of such securities. No one client owns
more than five percent of the securities of the Issuer.

ITEM 7  IDENTIFICATION AND CLARIFICATION OF THE SUBSIDIARY WHICH ACQUIRED THE
        SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY.

        Not Applicable.

ITEM 8  IDENTIFICATION AND CLARIFICATION OF MEMBERS OF THE GROUP.

        Not Applicable.

ITEM 9  NOTICE OF DISSOLUTION OF GROUP.

        Not Applicable.




                                       4
<PAGE>   5



ITEM 10 CERTIFICATION.

        By signing below I certify that, to the best of my knowledge and belief,
the securities referred to above were acquired in the ordinary course of
business and were not acquired for the purpose of and do not have the effect of
changing or influencing the control of the issuer of such securities and were
not acquired in connection with or as a participant in any transaction having
such purposes or effect.


                                    SIGNATURE

        After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


                                       Date: April 3, 1998




                                       /s/ THOMAS E. DUGGAN
                                       --------------------------------------
                                       General Counsel







                                       5



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