TRITON ENERGY LTD
424B5, 1998-12-02
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>   1
 
                                                Filed pursuant to rule 424(b)(5)
                                                      Registration No. 333-11703
                                                      Registration No. 333-67843
PROSPECTUS SUPPLEMENT
(TO PROSPECTUS DATED SEPTEMBER 25, 1998)
 
                                3,177,500 SHARES
 
                                  TRITON LOGO
 
                        8% CONVERTIBLE PREFERENCE SHARES
                            ------------------------
 
     Triton Energy Limited ("Triton") is distributing rights to purchase
approximately 3,177,500 shares of its 8% convertible preference shares to
holders of its ordinary shares and preference shares. You will have the right to
purchase, for a price of $70, one 8% convertible preference share for each right
distributed to you. You will also be able to purchase 8% convertible preference
shares that are not purchased by other shareholders. Triton will round up to the
nearest whole number the number of rights distributed to you.
 
<TABLE>
<S>                                             <C>
RIGHTS OFFERING                                 8% CONVERTIBLE PREFERENCE SHARES
- - Record Date -- November 30, 1998              - Conversion -- convertible into four ordinary
                                                  shares of Triton (subject to adjustments)
- - Number of rights you will receive for each
  of your:                                      - Redemption -- not redeemable before
                                                  September 30, 2001; redeemable on or after
  - ordinary shares -- .072                       September 30, 2001 if the market price of
                                                  Triton's ordinary shares meets certain
  - 5% convertible preference shares -- .072      targets
  - 8% convertible preference shares -- .288    - Dividends
- - Expiration Date -- December 22, 1998            - cumulative
- - Estimated proceeds to Triton (before            - payable semi-annually at the rate of 8%
  deducting expenses) -- $222,425,000               per year for each dividend period ending on
                                                    June 30 and December 31, beginning with the
                                                    June 30, 1999 dividend period
                                                  - payable in cash or additional 8% convertible
                                                    preference shares, at Triton's option
</TABLE>
 
     On September 30, 1998, HM4 Triton, L.P., an affiliate of Hicks, Muse, Tate
& Furst Incorporated, purchased 1,822,500 shares of Triton's 8% convertible
preference shares for $70 per share. HM4 Triton, L.P. has agreed to exercise all
of the rights it receives in the rights offering and to purchase any 8%
convertible preference shares not subscribed for in the rights offering (but not
more than 3,177,500 additional shares). HM4 Triton, L.P.'s obligations are
subject to certain customary closing conditions.
 
     Triton's ordinary shares are listed on the New York Stock Exchange under
the symbol "OIL." On November 23, 1998, the last reported sale price of the
ordinary shares on the New York Stock Exchange was $10 3/16 per share. The 8%
convertible preference shares may be listed on the New York Stock Exchange under
the symbol "OILPrA" if there is a sufficient number of holders to meet the
exchange's distribution requirements. Triton cannot assure you that these
requirements will be satisfied. The rights will be eligible to trade on the New
York Stock Exchange under the symbol "OIL RT" until the close of business on the
last trading day before the expiration date.
 
     SEE "RISK FACTORS" BEGINNING ON PAGE S-8 OF THIS PROSPECTUS SUPPLEMENT AND
PAGE 3 OF THE ACCOMPANYING PROSPECTUS FOR A DISCUSSION OF CERTAIN FACTORS THAT
YOU SHOULD CONSIDER BEFORE YOU INVEST IN THE 8% CONVERTIBLE PREFERENCE SHARES.
                            ------------------------
 
     THE SECURITIES AND EXCHANGE COMMISSION AND STATE SECURITIES REGULATORS HAVE
NOT APPROVED OR DISAPPROVED OF THESE SECURITIES OR DETERMINED THAT THIS
PROSPECTUS SUPPLEMENT OR THE ACCOMPANYING PROSPECTUS IS TRUTHFUL OR COMPLETE. IT
IS ILLEGAL FOR ANY PERSON TO TELL YOU OTHERWISE.
 
     Triton has retained Donaldson, Lufkin & Jenrette to act as the dealer
manager for the rights offering. Triton has agreed to pay them a customary fee,
to reimburse them for their reasonable out-of-pocket expenses and to indemnify
them against liabilities under the Securities Act of 1933 and some other
liabilities.
 
                    The dealer manager for this offering is:
 
                          DONALDSON, LUFKIN & JENRETTE
November 30, 1998
<PAGE>   2
 
     YOU SHOULD RELY ONLY ON THE INFORMATION CONTAINED IN THIS DOCUMENT OR THAT
WE HAVE REFERRED YOU TO. WE HAVE NOT AUTHORIZED ANYONE TO PROVIDE YOU WITH
INFORMATION THAT IS DIFFERENT. THIS PROSPECTUS SUPPLEMENT AND THE ACCOMPANYING
PROSPECTUS IS AN OFFER TO SELL OR TO BUY ONLY THE SHARES OFFERED HEREBY, BUT
ONLY UNDER CIRCUMSTANCES AND IN JURISDICTIONS WHERE IT IS LAWFUL TO DO SO. THE
INFORMATION CONTAINED IN THIS PROSPECTUS SUPPLEMENT AND THE ACCOMPANYING
PROSPECTUS IS CURRENT ONLY AS OF ITS DATE.
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                     PAGE
                                     ----
<S>                                  <C>
Prospectus Supplement
Questions and Answers About the
  Rights Offering..................    ii
Disclosure Regarding
  Forward-Looking Statements.......     v
Prospectus Summary.................   S-1
Risk Factors.......................   S-8
Use of Proceeds....................  S-12
Ratio of Earnings to Combined Fixed
  Charges and Preference
  Dividends........................  S-12
Price Range of Ordinary Shares and
  Dividend Policy..................  S-13
Capitalization.....................  S-14
The Rights Offering................  S-15
Investment by Hicks Muse...........  S-24
Description of the 8% Preference
  Shares...........................  S-30
Certain U.S. Federal Income Tax
  Considerations...................  S-37
</TABLE>
 
<TABLE>
<CAPTION>
                                     PAGE
                                     ----
<S>                                  <C>
Prospectus
Available Information..............     2
Incorporation of Certain Documents
  by Reference.....................     2
Enforceability of Civil Liabilities
  Against Foreign Persons..........     3
The Company........................     3
Risk Factors.......................     3
Use of Proceeds....................     6
Ratios of Earnings to Fixed Charges
  and Earnings to Combined Fixed
  Charges and Preference
  Dividends........................     6
Description of Debt Securities.....     7
Description of Share Capital of
  TEL..............................    17
Description of Warrants............    23
Plan of Distribution...............    23
Legal Matters......................    24
Experts............................    24
</TABLE>
 
                                        i
<PAGE>   3
 
                QUESTIONS AND ANSWERS ABOUT THE RIGHTS OFFERING
 
Q:   WHAT IS A RIGHT?
 
     Each right enables you to purchase an 8% convertible preference share for
     $70 per share in cash.
 
Q:   HOW MANY RIGHTS WILL I RECEIVE?
 
     You will receive .072 rights for each ordinary share and each 5%
     convertible preference share that you own and .288 rights for each 8%
     convertible preference share that you own. You will receive a certificate
     evidencing the rights.
 
Q:   CAN I BUY MORE 8% CONVERTIBLE PREFERENCE SHARES THAN THE NUMBER OF RIGHTS
     THAT I RECEIVE?
 
     If other holders of the rights do not fully exercise their rights to
     subscribe for 8% convertible preference shares, you will have the right to
     subscribe for the unsold 8% convertible preference shares so long as you
     fully exercise your basic right to subscribe for 8% convertible preference
     shares. If there are not enough shares to satisfy all subscriptions for
     additional shares, the available shares will be distributed pro rata among
     the holders requesting to purchase additional shares based on the number of
     rights exercised by each holder pursuant to their basic subscription right.
     You will receive a refund of your money, without interest, for any
     additional shares that you subscribed for but were unable to purchase.
 
Q:   HOW DO I EXERCISE MY RIGHTS TO PURCHASE THE 8% CONVERTIBLE PREFERENCE
     SHARES?
 
     You can exercise your rights by filling out and signing the certificate
     evidencing the rights and sending it with your payment for all of the 8%
     convertible preference shares that you wish to subscribe for to ChaseMellon
     Shareholder Services, L.L.C. at its address (which is on the back cover of
     this prospectus supplement) before the expiration date. The rights
     certificate that you will receive includes a box which you may check if you
     wish to exercise your right to purchase more 8% convertible preference
     shares than you subscribed for pursuant to your basic subscription right.
     If you elect to do so, you will be required to include payment in full for
     all additional 8% convertible preference shares which you wish to purchase.
 
Q:   WHEN IS THE EXPIRATION DATE?
 
     5:00 p.m., New York City time, on December 22, 1998.
 
Q:   CAN I CHANGE MY MIND ONCE I HAVE SUBSCRIBED?
 
     No. Once you exercise your right to subscribe for 8% convertible preference
     shares, you may not revoke your exercise.
 
Q:   WHAT HAPPENS IF I DO NOT EXERCISE MY RIGHTS?
 
     If you do not exercise your rights before the expiration date, your rights
     will expire and will be void.
 
Q:   WILL FEWER THAN 3,177,500 SHARES OF 8% CONVERTIBLE PREFERENCE SHARES BE
     ISSUED IF ALL OF THE RIGHTS ARE NOT EXERCISED?
 
     An affiliate of Hicks, Muse, Tate & Furst Incorporated has agreed to
     purchase any 8% convertible preference shares that are not purchased by the
     holders of rights.
 
                                       ii
<PAGE>   4
     However, its obligations are subject to the satisfaction of certain
     conditions described on page S-24.
 
Q:   CAN I TRANSFER MY RIGHTS?
 
     If a market for the rights develops, you may purchase or sell rights
     through the typical methods of selling securities. The rights will be
     eligible to trade on the New York Stock Exchange until the close of
     business on the last trading day before the expiration date. Triton does
     not know if investor interest will lead to the development of a trading
     market for the rights, how liquid any market may be, the price at which the
     rights may trade or how long any market might last.
 
Q:   WILL THE 8% CONVERTIBLE PREFERENCE SHARES BE LISTED ON A STOCK EXCHANGE?
 
     The 8% convertible preference shares have been approved by the New York
     Stock Exchange for listing, subject to official notice of issuance and the
     satisfaction of the minimum distribution requirements of the exchange,
     under the symbol "OILPrA." Because the current market price for the
     ordinary shares is significantly below the conversion price of the 8%
     convertible preference shares, there is a substantial risk that not enough
     holders will exercise their rights to satisfy the minimum distribution
     requirements. Even if the 8% convertible preference shares are listed on
     the New York Stock Exchange, Triton does not know if investor interest will
     lead to the development of a trading market for the shares, how liquid any
     market may be or the price at which the shares may trade. For a description
     of the market risks associated with a purchase of the 8% convertible
     preference shares, see "Risk Factors -- Market Considerations" on page S-9.
 
Q:   WILL THE 8% CONVERTIBLE PREFERENCE SHARES HAVE VOTING RIGHTS?
 
     Yes. If you own 8% convertible preference shares, you will be able to vote
     with the holders of ordinary shares on all matters brought before Triton's
     shareholders. You will have a number of votes equal to the number of whole
     ordinary shares into which your 8% convertible preference shares could have
     been converted on the relevant record date. On matters that only require
     approval by holders of 8% convertible preference shares, you will have one
     vote for each share you hold.
 
Q:   WILL I BE ABLE TO CONVERT MY 8% CONVERTIBLE PREFERENCE SHARES INTO ORDINARY
     SHARES AT ANY TIME?
 
     You will generally be able to convert your 8% convertible preference shares
     at any time. Initially, each 8% convertible preference share will be
     convertible into four ordinary shares.
 
Q:   WILL TRITON BE ABLE TO REDEEM THE 8% CONVERTIBLE PREFERENCE SHARES?
 
     Triton cannot redeem the 8% convertible preference shares until September
     30, 2001, and then Triton may only redeem the 8% convertible preference
     shares if the market price of the ordinary shares is above certain levels
     described on page S-35.
 
Q:   WILL I RECEIVE DIVIDENDS ON THE 8% CONVERTIBLE PREFERENCE SHARES?
 
     Yes. You will be entitled to receive a semi-annual dividend at a rate of 8%
     per year of the stated value per share (initially $70). Triton will pay
     this dividend for each dividend period ending on June 30 and December 31 of
     each year, beginning with the dividend period ending on June 30, 1999.
     Triton can pay dividends in cash or
 
                                       iii
<PAGE>   5
     additional 8% convertible preference shares, at its option. You may realize
     income or gain when you receive dividends, regardless of whether they are
     paid in cash or additional shares.
 
Q:   WHAT WILL TRITON USE THE PROCEEDS OF THE RIGHTS OFFERING FOR?
 
     Triton will use the proceeds to repay indebtedness outstanding under its
     credit facilities, to continue funding its operations in Colombia and for
     other general corporate purposes.
 
Q:   WHERE CAN I FIND MORE INFORMATION?
 
     You may obtain more information from the sources described under "Available
     Information" in the prospectus attached to this prospectus supplement. You
     also may contact the Information Agent at its address and telephone number
     on the back cover page of this prospectus supplement for more information
     or additional copies of this prospectus supplement or any of the enclosed
     forms.
 
                                       iv
<PAGE>   6
 
                DISCLOSURE REGARDING FORWARD-LOOKING STATEMENTS
 
     Certain statements in this prospectus supplement or in the documents we
refer you to, including expectations, intentions, plans and beliefs of Triton
and management, are forward-looking statements, as defined in Section 21E of the
Securities Exchange Act of 1934, as amended, that depend on certain events,
risks and uncertainties that may be outside Triton's control. These
forward-looking statements include statements of management's plans and
objectives for future operations and statements of future economic performance;
information regarding drilling schedules and schedules for the start-up of
production facilities; expected or planned production or transportation
capacity; when the Cusiana and Cupiagua fields in Colombia might become
self-financing; future production of the Cusiana and Cupiagua fields; the
negotiation of a gas-sales contract and commencement of production in
Malaysia-Thailand; Triton's capital budget and future capital requirements;
Triton's ability to meet its future capital needs; the amount by which
production from the Cusiana and Cupiagua fields may increase or when such
increased production may begin; Triton's realization of its deferred tax asset;
the level of future expenditures for environmental costs; the outcome of
regulatory and litigation matters; the impact of Year 2000 issues; the amount of
proved oil and gas reserves and discounted future net cash flows therefrom; and
the assumptions described in this prospectus supplement or in the documents we
refer you to underlying such forward-looking statements. Actual results and
developments could differ materially from those expressed in or implied by such
statements due to a number of factors, including those set forth under the
caption "Risk Factors" in the accompanying prospectus and in Notes 19 and 20 to
Triton's consolidated financial statements included in Triton's Annual Report on
Form 10-K incorporated by reference herein.
 
                                        v
<PAGE>   7
 
                               PROSPECTUS SUMMARY
 
     This summary highlights selected information from this document and may not
contain all of the information you should consider before investing in the 8%
convertible preference shares. You should carefully read this entire document
and the documents we refer you to. See "Incorporation of Certain Documents by
Reference" in the accompanying prospectus (page 2). The distribution of the
rights and sale of 8% convertible preference shares are sometimes referred to in
this prospectus supplement as the "Rights Offering." "Triton" refers to Triton
and its consolidated subsidiaries.
 
TRITON ENERGY LIMITED
 
Caledonian House
Mary Street
P.O. Box 1043
George Town, Grand Cayman, Cayman Islands
(345) 949-0050
 
     Triton is an international oil and gas exploration and production company.
Triton's principal properties, operations and oil and gas reserves are located
in Colombia and Malaysia-Thailand. Triton is actively exploring for oil and gas
in these areas, as well as in Southern Europe, Africa and the Middle East.
 
     Triton was formed in the Cayman Islands in 1995 and became the parent
holding company of Triton Energy Corporation through the merger of a subsidiary
of Triton with Triton Energy Corporation in 1996. In connection with the merger,
each share of common stock of Triton Energy Corporation was converted into one
ordinary share of Triton.
 
INVESTMENT BY HM4 TRITON, L.P. (PAGE S-24)
 
     On August 31, 1998, Triton entered into a stock purchase agreement with HM4
Triton, L.P., an affiliate of Hicks, Muse, Tate & Furst Incorporated. Under the
stock purchase agreement, on September 30, 1998, HM4 Triton, L.P. purchased
1,822,500 8% convertible preference shares for $70 per share or a total purchase
price of $127,575,000. Also on that date, the size of Triton's Board of
Directors was reduced from eleven to ten, five directors resigned and four
directors nominated by HM4 Triton, L.P. were elected. Triton used the net
proceeds of the HM4 Triton, L.P. investment to reduce indebtedness and for
general corporate purposes.
 
     The stock purchase agreement with HM4 Triton, L.P. requires Triton to
engage in this Rights Offering. On or soon after Triton completes the Rights
Offering the following events are expected to happen:
 
     - Sale of 8% Convertible Preference Shares. Triton will issue and sell up
       to approximately 3,177,500 8% convertible preference shares to investors
       who subscribe to purchase 8% convertible preference shares in the Rights
       Offering.
 
     - Agreement to Purchase Excess Shares. In the stock purchase agreement, HM4
       Triton, L.P. agreed to exercise the 524,880 rights that it will receive
       in the Rights Offering for its 1,822,500 8% convertible preference
       shares. HM4 Triton, L.P. also agreed to purchase any 8% convertible
       preference shares not purchased in the Rights Offering (up to a maximum
       of 3,177,500 shares, including the 524,880
                                       S-1
<PAGE>   8
 
       shares it has agreed to purchase in the Rights Offering, but excluding
       the 1,822,500 shares previously purchased), at the same $70 per share
       price at which rights holders may subscribe to purchase 8% convertible
       preference shares. HM4 Triton, L.P.'s obligations are subject to the
       satisfaction of certain closing conditions described on page S-24.
       Whether or not HM4 Triton, L.P. purchases any shares, you will still be
       obligated to purchase any shares you subscribe for in the rights
       offering.
 
                              THE RIGHTS OFFERING
 
Rights (Page S-15)..............    If you hold of record ordinary shares or 5%
                                    convertible preference shares at the close
                                    of business on November 30, 1998, you will
                                    receive .072 transferable rights for each
                                    ordinary share or 5% convertible preference
                                    share. If you hold of record 8% convertible
                                    preference shares at the close of business
                                    on November 30, 1998, you will receive .288
                                    transferable rights for each 8% convertible
                                    preference share. Triton will not distribute
                                    fractions of rights and will not pay any
                                    cash instead of fractions of rights.
                                    Instead, Triton will round the number of
                                    rights distributed to each holder of
                                    ordinary shares, 5% convertible preference
                                    shares and 8% convertible preference shares
                                    up to the nearest whole number.
                                    Approximately 3,177,500 rights will be
                                    distributed in this Rights Offering.
                                    Approximately 3,177,500 8% convertible
                                    preference shares will be sold upon exercise
                                    of the rights if all rights are fully
                                    exercised.
 
Right to Purchase 8% Convertible
  Preference Shares (Page
  S-15).........................    You can purchase one 8% convertible
                                    preference share for one right plus $70 in
                                    cash.
 
Right to Purchase Unsold 8%
  Convertible Preference Shares
  (Page S-16)...................    If you fully exercise your basic right to
                                    subscribe for 8% convertible preference
                                    shares, you may also subscribe for
                                    additional 8% convertible preference shares
                                    that may become available because some
                                    holders of rights do not fully exercise
                                    their rights. If there are not enough shares
                                    to satisfy all of the subscriptions for
                                    additional shares, the available shares will
                                    be distributed pro rata among holders
                                    requesting to purchase additional shares,
                                    based on the number of rights exercised by
                                    each holder pursuant to their basic
                                    subscription right.
 
Purchase Price (Page S-16)......    $70 in cash per 8% convertible preference
                                    share.
                                       S-2
<PAGE>   9
 
Expiration Date (Page S-16).....    5:00 p.m., New York City time, on December
                                    22, 1998 (unless Triton extends the
                                    expiration date). If you do not exercise
                                    your rights before the expiration date, your
                                    rights will be void and you will not be able
                                    to exercise your rights in the future.
 
How to Exercise Your Rights
  (Page S-17)...................    You may exercise your rights by properly
                                    completing and signing the subscription
                                    certificate representing the rights and
                                    sending it (or following the guaranteed
                                    delivery procedures), with payment of $70
                                    for each 8% convertible preference share
                                    subscribed for (including any unsold shares
                                    you wish to subscribe for pursuant to your
                                    oversubscription privilege), to ChaseMellon
                                    Shareholder Services, L.L.C., which is
                                    acting as subscription agent, on or before
                                    the expiration date. If you send
                                    subscription certificates by mail, we
                                    recommend that you use insured, registered
                                    mail. Triton will not pay interest on funds
                                    delivered in payment of the purchase price.
                                    You will receive a refund of your money,
                                    without interest, for any additional shares
                                    you subscribed for but were unable to
                                    purchase.
 
NO REVOCATION (Page S-20).......    IF YOU EXERCISE YOUR RIGHT TO
                                    PURCHASE 8% CONVERTIBLE PREFERENCE SHARES,
                                    YOU MAY NOT REVOKE THAT EXERCISE, EVEN IF
                                    HM4 TRITON, L.P. DOES NOT ULTIMATELY
                                    PURCHASE ANY SHARES.
 
Transferability of Rights (Page
  S-20).........................    You may transfer the rights by following the
                                    instructions to the subscription
                                    certificate. You may also sell your rights
                                    through your bank or broker, to the extent
                                    that a market for the rights develops. The
                                    rights will be eligible to trade on the New
                                    York Stock Exchange until the close of
                                    business on the last New York Stock Exchange
                                    trading day before the expiration date.
                                    Triton does not know the extent to which
                                    investor interest will lead to the
                                    development of a trading market for the
                                    rights, how liquid that market might be, the
                                    price at which the rights may trade or how
                                    long any market might last.
                                       S-3
<PAGE>   10
 
Agreements of HM4 Triton, L.P.
  (Page S-24)...................    In the stock purchase agreement, HM4
                                    Triton, L.P. agreed to exercise the 524,880
                                    rights which it will receive in the Rights
                                    Offering for its 8% convertible preference
                                    shares. HM4 Triton, L.P. also agreed to
                                    purchase any 8% convertible preference
                                    shares that are not purchased in the Rights
                                    Offering (up to a maximum of 3,177,500
                                    shares, including the 524,880 shares it has
                                    agreed to purchase in the Rights Offering,
                                    but excluding the 1,822,500 shares
                                    previously purchased) after all shareholders
                                    are given the right to purchase shares that
                                    are not subscribed for, also at a price of
                                    $70 per share. In the stock purchase
                                    agreement, HM4 Triton, L.P. agreed not to
                                    exercise the oversubscription privilege with
                                    respect to any rights it receives. HM4
                                    Triton, L.P.'s obligations are subject to
                                    the satisfaction of certain conditions
                                    described on page S-24. It is not a
                                    condition to your obligation to purchase
                                    shares you subscribe for that HM4 Triton
                                    L.P. ultimately purchase any shares. If you
                                    exercise your rights, you will continue to
                                    be obligated to purchase any 8% convertible
                                    preference shares that you subscribe for
                                    whether or not HM4 Triton, L.P. purchases
                                    any shares.
 
Terms of 8% Convertible
  Preference Shares (Page S-30)...  Conversion. You will generally have the
                                    right to convert your 8% convertible
                                    preference shares into ordinary shares at
                                    any time before redemption at the conversion
                                    price in effect at the time of conversion.
                                    The initial conversion price is $17.50 per
                                    ordinary share. Each 8% convertible
                                    preference share will initially be
                                    convertible into four ordinary shares
                                    (subject to adjustment under certain
                                    circumstances described in this prospectus
                                    supplement). The last reported sale price of
                                    the ordinary shares on the New York Stock
                                    Exchange on November 23, 1998 was $10 3/16
                                    per share.
 
                                    Dividends. Dividends on the 8% convertible
                                    preference shares will be cumulative from
                                    the date the shares are first issued. Triton
                                    will be required to pay dividends
                                    semi-annually at the rate of 8% per year of
                                    the stated value per share (initially $70)
                                    for each semi-annual dividend period ending
                                    on June 30 and December 31 of each year,
                                    beginning with the dividend period ending on
                                    June 30, 1999.
                                       S-4
<PAGE>   11
                                    Triton will pay dividends no later than five
                                    days after the end of a dividend period.
                                    Triton can choose to pay dividends in cash
                                    or in additional 8% convertible preference
                                    shares, if legally available. If dividends
                                    are not paid in cash or in additional shares
                                    on a scheduled dividend payment date, all
                                    accumulated but unpaid dividends will be
                                    added to the stated value of the 8%
                                    convertible preference shares outstanding,
                                    and future dividends will accumulate and be
                                    paid based on the stated value, as adjusted.
 
                                    Redemption. Triton cannot redeem the 8%
                                    convertible preference shares before
                                    September 30, 2001. Beginning September 30,
                                    2001, Triton can redeem all, but not less
                                    than all, of the outstanding 8% convertible
                                    preference shares at any time if the average
                                    market value of the ordinary shares is above
                                    certain market values specified in this
                                    prospectus supplement. The redemption price
                                    will be equal to $70 per share, plus an
                                    amount equal to all accumulated but unpaid
                                    dividends, and will be payable in cash.
 
                                    Liquidation. The liquidation preference of
                                    the 8% convertible preference shares is $70
                                    per share, plus accumulated and unpaid
                                    dividends.
 
                                    Voting Rights. The holders of the 8%
                                    convertible preference shares will generally
                                    vote with the holders of the ordinary shares
                                    on all matters brought before Triton's
                                    shareholders. In addition, a class vote of
                                    the 8% preference shares will be required in
                                    certain limited circumstances. The holders
                                    of the 8% convertible preference shares will
                                    also be entitled to elect two directors of
                                    Triton if Triton does not pay dividends on
                                    the 8% convertible preference shares under
                                    certain circumstances. When voting with the
                                    holders of the ordinary shares, the holders
                                    of the 8% convertible preference shares will
                                    have the number of votes for each share that
                                    they would have if they had converted their
                                    shares into ordinary shares on the related
                                    record date. When voting as a class, the
                                    holders of the 8% convertible preference
                                    shares will have one vote per share.
 
                                    Ownership Percentages. After the Rights
                                    Offering, the 8% convertible preference
                                    shares will be equal to approximately 35% of
                                    the total ordinary shares
                                       S-5
<PAGE>   12
                                    outstanding (assuming the conversion into
                                    ordinary shares of all outstanding
                                    convertible securities other than stock
                                    options and before giving effect to the
                                    payment of any dividends in additional 8%
                                    convertible preference shares).
 
Certain U.S. Federal Income Tax
  Considerations (Page S-37)....    Consequences to Holders of Ordinary Shares.
                                    Triton intends to take the position that you
                                    will not recognize taxable income when the
                                    rights are issued. However, you will realize
                                    gain or loss if you sell the rights or the
                                    8% convertible preference shares you acquire
                                    by exercising the rights. You generally will
                                    also realize income or gain when you receive
                                    dividends.
 
                                    Consequences to Holders of 5% Convertible
                                    Preference Shares. The value, if any, of the
                                    rights you receive will be treated as a
                                    taxable dividend to the extent this value is
                                    less than or equal to Triton's earnings and
                                    profits. Any value in excess of Triton's
                                    earnings and profits will be treated as a
                                    nontaxable reduction in the tax basis of the
                                    5% convertible preference shares. Any value
                                    in excess of the tax basis will be taxed as
                                    a capital gain. You will also realize gain
                                    or loss if you sell the rights or the 8%
                                    convertible preference shares you acquire by
                                    exercising the rights, and you generally
                                    will realize income or gain when you receive
                                    dividends.
 
Use of Proceeds (Page S-12).....    The net proceeds from this Rights Offering
                                    will be approximately $214 million (based on
                                    the assumptions discussed on page S-12 under
                                    "Use of Proceeds"). Triton will use the net
                                    proceeds to repay indebtedness outstanding
                                    under its credit facilities, to continue
                                    funding Triton's obligations relating to the
                                    development of its operations in Colombia
                                    and for general corporate purposes.
 
NYSE Symbols....................    The ordinary shares are traded on the New
                                    York Stock Exchange under the symbol "OIL."
                                    The rights will be eligible to trade on the
                                    New York Stock Exchange under the symbol
                                    "OIL RT." Triton does not know whether a
                                    trading market will develop for the rights.
                                    The 8% convertible preference shares have
                                    been approved for listing on the New York
                                    Stock Exchange under the symbol "OILPrA,"
                                    subject to meeting the New York Stock
                                    Exchange minimum distribution requirements.
                                    Triton cannot assure you that the 8%


                                       S-6
<PAGE>   13
 
                                    convertible preference shares will meet the
                                    distribution requirements.
 
Dealer Manager..................    Donaldson, Lufkin & Jenrette Securities
                                    Corporation will be the dealer manager for 
                                    the Rights Offering. Triton has agreed to
                                    pay the dealer manager a customary fee and
                                    to reimburse the dealer manager for its
                                    reasonable out-of-pocket expenses. Triton
                                    has also agreed to indemnify the dealer
                                    manager against liabilities under the
                                    Securities Act of 1933 and certain other
                                    liabilities.
 
Risk Factors....................    See "Risk Factors" beginning on page S-8 of
                                    this prospectus supplement and page 3 of the
                                    accompanying prospectus for a discussion of
                                    certain factors that you should consider
                                    before you invest in the 8% convertible
                                    preference shares.


                                       S-7
<PAGE>   14
 
                                  RISK FACTORS
 
INFLUENCE BY HM4 TRITON, L.P.
 
     After HM4 Triton, L.P. purchased 1,822,500 8% convertible preference shares
on September 30, 1998, Triton decreased the size of its Board of Directors from
eleven to ten directors, five directors resigned and the Board of Directors
appointed four persons nominated by HM4 Triton, L.P. to fill the vacancies.
Under a shareholders agreement, HM4 Triton, L.P. has the right to designate
nominees for election to the Triton Board so long as it has specified ownership
levels of Triton shares. In the shareholders agreement, Triton also agreed that
it would not take certain fundamental corporate actions, including entering into
any merger or sale of substantial assets, without HM4 Triton, L.P.'s consent.
Triton cannot be sure of the effect that HM4 Triton, L.P.'s influence on and
participation in the management of Triton will have on Triton's financial
condition and results of operations.
 
     In addition to the 1,822,500 8% convertible preference shares purchased by
HM4 Triton, L.P. on September 30, 1998, as of November 24, 1998, HM4 Triton,
L.P. had purchased 1,318,000 ordinary shares in open market transactions.
Collectively, the 8% convertible preference shares and ordinary shares held by
HM4 Triton, L.P. represent approximately 20% of Triton's outstanding voting
shares. In addition, if the rights distributed in the Rights Offering are not
fully exercised, HM4 Triton, L.P. has agreed to buy any 8% convertible
preference shares that are not purchased by the exercise of rights in the Rights
Offering, up to a maximum of 3,177,500 shares (including the 524,880 8%
convertible preference shares HM4 Triton, L.P. has agreed to purchase pursuant
to the rights distributed to it in the Rights Offering, but excluding the
1,822,500 shares previously purchased). If no rights are exercised by other
shareholders in the Rights Offering, HM4 Triton, L.P. will obtain beneficial
ownership of approximately 38% of Triton's voting shares. Even if all of the
rights are exercised, HM4 Triton, L.P. will beneficially own approximately 20%
of the outstanding voting shares and therefore will be in a position to
influence actions that require the consent of Triton's shareholders. As a result
of the factors described above, HM4 Triton, L.P. has significant influence over
the actions of Triton's Board and will be able to influence and, in certain
cases, determine the outcome of matters submitted for the approval of Triton's
shareholders. HM4 Triton, L.P. is not restricted from further increasing its
ownership of Triton's capital stock either prior to or after completion of the
Rights Offering, and, subject to any legal requirements, HM4 Triton, L.P. may
acquire additional shares of such stock through open market purchases or other
transactions.
 
     The existence of HM4 Triton, L.P. as a shareholder of Triton may make it
more difficult for a third party to acquire, or discourage a third party from
seeking to acquire, a majority of the outstanding ordinary shares. A third party
would be required to negotiate any such transaction with HM4 Triton, L.P., and
the interests of that entity as a shareholder may be different from the
interests of the other Triton shareholders.
 
     If a sufficient number of holders of ordinary shares do not exercise their
rights in the Rights Offering, HM4 Triton, L.P. could hold a majority (or even
two-thirds) of the 8% convertible preference shares outstanding after the Rights
Offering. If HM4 Triton, L.P. were to hold a simple majority of the outstanding
8% convertible preference shares, it could, among other things, approve the
creation of other classes of shares ranking equally with the 8% convertible
preference shares. If HM4 Triton, L.P. were to hold two-thirds of
 
                                       S-8
<PAGE>   15
 
the outstanding 8% convertible preference shares, it could, among other things,
approve changes to the terms of the 8% convertible preference shares, the
creation of other classes of shares ranking senior to the 8% convertible
preference shares or charter amendments that materially adversely affect the
rights of all holders of 8% convertible preference shares.
HM4 Triton, L.P.'s interests as a holder of 8% convertible preference shares may
be different from the interests of other holders of 8% convertible preference
shares.
 
MANAGEMENT AND STRATEGIC CHANGES
 
     On October 2, 1998, Triton announced that its Board of Directors had
elected James C. Musselman as President and Interim Chief Executive Officer and
Robert B. Holland, III as Chief Operating Officer of Triton. The Board intends
to continue its search for a permanent Chief Executive Officer of Triton. Triton
cannot be sure that the permanent Chief Executive Officer will not make further
changes in Triton's management and/or the ultimate business strategy Triton will
adopt. In addition, management has begun implementing a more focused exploration
effort and is considering a number of operating alternatives, which could
include potential strategic combinations with domestic or international
entities.
 
CONVERSION PRICE OF 8% CONVERTIBLE PREFERENCE SHARES
 
     The conversion price of the 8% convertible preference shares ($17.50 per
ordinary share) currently is significantly above the market price of ordinary
shares ($10 3/16 per share closing price as of November 23, 1998). Triton cannot
assure you that the market price of the ordinary shares will at any time be
equal to or more than the conversion price of the 8% convertible preference
shares.
 
MARKET CONSIDERATIONS
 
     Rights. Although the rights will be eligible to trade on the New York Stock
Exchange, Triton does not know the extent to which investor interest will lead
to the development of a trading market for the rights, how liquid that market
might be or the price at which the rights may trade. The dealer manager expects
that if investor interest leads to the development of a trading market for the
rights, it will make a market in the rights, but it is not obligated to do so.
The dealer manager may discontinue any market making activity at any time.
 
     8% Convertible Preference Shares. The $70 purchase price for the 8%
convertible preference shares was determined by Triton through negotiations with
HM4 Triton, L.P. On August 31, 1998, when Triton and HM4 Triton, L.P. entered
into the stock purchase agreement, the closing price for the ordinary shares was
$12 1/8. As of November 23, 1998, the closing price of the ordinary shares was
$10 3/16. The trading values of the 8% convertible preference shares will most
likely be based on the market price of the underlying ordinary shares and the
value given to the dividend rights and other preferences of the 8% convertible
preference shares. Therefore, if the market price of the ordinary shares does
not increase, the 8% convertible preference shares will most likely trade, if at
all, at a price that is less than the $70 per share purchase price you will pay.
 
     There is currently no public market for the 8% convertible preference
shares. The 8% convertible preference shares have been approved for listing on
the New York Stock Exchange, but the approval is subject to official notice of
issuance and satisfaction of minimum distribution requirements. Because, as
noted above, the market price for the ordinary shares is currently significantly
below the conversion price of the 8% convertible
 
                                       S-9
<PAGE>   16
 
preference shares, there is a substantial risk that not enough holders will
exercise their rights to satisfy the minimum distribution requirements. Even if
the 8% convertible preference shares are listed on the New York Stock Exchange,
Triton does not know if a public market for the shares will develop, how liquid
any market may be or the price at which the 8% convertible preference shares may
trade.
 
     Triton cannot assure you that the market price of the ordinary shares will
not decline during the subscription period or that, after the 8% convertible
preference shares are issued upon exercise of rights, a subscribing rights
holder will be able to sell 8% convertible preference shares purchased in the
Rights Offering at a price equal to or greater than the purchase price paid in
the Rights Offering. The market price of the 8% convertible preference shares
could vary significantly in response to Triton's operating results and other
factors, including the size of the public float of the 8% convertible preference
shares (which will depend in part on the percentage of the rights that are
exercised by parties other than HM4 Triton, L.P. in the Rights Offering).
 
IRREVOCABILITY OF SUBSCRIPTIONS
 
     You cannot revoke your election to exercise rights. However, HM4 Triton,
L.P.'s obligation to purchase additional 8% convertible preference shares is
subject to certain conditions being satisfied. If you exercise your rights, your
obligation to purchase 8% convertible preference shares subscribed for will not
be conditioned on HM4 Triton, L.P. purchasing any additional shares. You will
continue to be obligated to purchase any shares you subscribe for whether or not
HM4 Triton, L.P. purchases any additional shares. Until you receive certificates
representing 8% convertible preference shares, you may not be able to sell those
shares. Certificates representing 8% convertible preference shares purchased in
the Rights Offering will be delivered by mail as soon as practicable following
the expiration date. Triton will not pay you interest on money you send to the
subscription agent when you exercise your rights before certificates for the 8%
convertible preference shares are delivered or on money refunded to you if you
are unable to purchase any additional shares subscribed for.
 
DIVIDENDS
 
     Triton may choose to pay any dividends on the 8% convertible preference
shares in cash or in additional 8% convertible preference shares.
 
LIQUIDITY
 
     Triton is continuing its efforts to reduce its general and administrative
expenses and exploration expenditures. Nevertheless, Triton expects that cash
from operating activities in 1999 will not be sufficient to cover all of its
capital needs for 1999.
 
     For internal planning purposes, Triton is assuming that the West Texas
Intermediate oil price will average $14 per barrel in 1999, that daily oil
production from the Cusiana and Cupiagua fields in 1999 will average
approximately 430,000 barrels per day, that Triton's share of capital
expenditures in Colombia will be approximately $85 million to $90 million (as
currently estimated by the operator) and that Triton will be successful in
reducing its exploration commitments by approximately one half. Based on these
assumptions, Triton expects that it will spend at least $100 million to $125
million more in cash in 1999 than it generates from operating activities. Triton
expects to fund the shortfall
 
                                      S-10
<PAGE>   17
 
by a combination of cash on hand and proceeds from the Rights Offering. These
assumptions may not prove to be valid or other factors may materially affect
Triton's cash position. If the Rights Offering is not consummated, Triton
expects that it will be required to seek alternative sources of capital in early
1999.
 
ANTI-TAKEOVER PROVISIONS
 
     In addition to the influence of HM4 Triton as described above, Triton's
Articles of Association include provisions that may make it more difficult for a
third party to acquire, or discourage a third party from seeking to acquire, a
majority of the outstanding ordinary shares. Triton can issue approximately
eight million preference shares with rights and preferences determined by the
Board of Directors without any shareholder approval. Triton's directors are
divided into three classes and only one class is elected each year. HM4 Triton,
L.P. also has the right to designate nominees for election to the Triton Board
so long as HM4 Triton L.P. has specified ownership levels of Triton shares.
These factors will make it difficult for a third party to replace Triton's
entire Board. Triton also has a shareholder rights plan which gives shareholders
the right to purchase ordinary shares of Triton for one-half of their per share
market value if a third party acquires beneficial ownership of 15% or more of
the ordinary shares (although HM4 Triton, L.P.'s ability to acquire shares is
unlimited unless its ownership decreases below certain levels.) This would
result in significant economic dilution in any third party's investment.
Finally, under Cayman Islands law, a business combination generally requires the
affirmative vote of two-thirds of the shareholders voting.
 
CERTAIN U.S. FEDERAL INCOME TAX CONSIDERATIONS FOR U.S. PERSONS
 
     Consequences to holders of ordinary shares. Triton intends to take the
position that you will not recognize taxable income when the rights are issued.
However, the tax treatment of the distribution of rights to you is uncertain,
and you should contact your tax advisor about the receipt, exercise and sale of
the rights and the sale or redemption of the 8% convertible preference shares
you acquire by exercising the rights. You will realize gain or loss if you sell
the rights.
 
     Consequences to holders of 5% Convertible Preference Shares. The value of
the rights you receive, if any, will be treated as a taxable dividend to the
extent that the value is less than or equal to Triton's earnings and profits.
Any value in excess of Triton's earnings and profits will be treated as a
nontaxable reduction in the tax basis of the 5% convertible preference shares.
Any value in excess of the tax basis will be taxed as a capital gain. You will
realize gain or loss if you sell the rights.
 
     Consequences of acquiring 8% Convertible Preference Shares. If you acquire
8% convertible preference shares by exercising the rights you receive, you
should contact your tax advisor about the tax implications of receiving
dividends on those shares, of Triton's redemption of those shares, of converting
those shares into ordinary shares and of selling those shares. You will realize
gain or loss if you sell the 8% convertible preference shares you acquire by
exercising the rights, and you generally will realize income or gain when you
receive dividends. For example, if you receive a dividend paid in kind, you must
include the fair market value of that dividend in gross income for U.S. federal
income tax purposes, even though you did not receive any cash.
 
                                      S-11
<PAGE>   18
 
                                USE OF PROCEEDS
 
     The net proceeds to be received by Triton from the sale of the 8%
convertible preference shares, par value $.01 per share (the "8% Preference
Shares"), are estimated to be approximately $214 million, after deducting
expenses payable by Triton of approximately $5.6 million (assuming HM4 Triton,
L.P. purchases the maximum number of 8% Preference Shares) and a partial
dividend of $2.4 million to HM4 Triton, L.P. See "Investment by Hicks
Muse -- Payment of Expenses and Additional Fees" and "Description of the 8%
Preference Shares -- Dividends." The net proceeds from the sale of the 8%
Preference Shares will be used to repay indebtedness outstanding under Triton's
credit facilities at the time the sale is consummated, to continue funding
Triton's obligations relating to the development of its operations in Colombia
and to meet general corporate needs, including possible future acquisitions. As
of November 23, 1998, there was an aggregate of $10 million outstanding under
the credit facilities, currently bearing interest at an average rate of 6.65%
per annum and maturing from March 1999 through May 1999.
 
                  RATIO OF EARNINGS TO COMBINED FIXED CHARGES
                            AND PREFERENCE DIVIDENDS
 
     For purposes of computing the ratio of earnings to combined fixed charges
and preference dividends, earnings consist of earnings (loss) from continuing
operations before income taxes, minority interest, extraordinary items and
cumulative effect of accounting changes, plus fixed charges (interest charges
and preference share dividend requirements of Triton and its subsidiaries,
adjusted to a pretax basis), less interest capitalized, less preference share
dividend requirements of Triton and its subsidiaries adjusted to a pretax basis
and less undistributed earnings of affiliates whose debt is not guaranteed by
Triton.
 
     The following table sets forth the ratio of earnings to combined fixed
charges and preference dividends for Triton for the periods indicated:
 
<TABLE>
<CAPTION>
                           NINE MONTHS                            SEVEN
                              ENDED           YEAR ENDED          MONTHS      YEAR ENDED
                          SEPTEMBER 30,      DECEMBER 31,         ENDED         MAY 31,
                          -------------   ------------------   DECEMBER 31,   -----------
                          1998    1997    1997   1996   1995       1994       1994   1993
                          -----   -----   ----   ----   ----   ------------   ----   ----
<S>                       <C>     <C>     <C>    <C>    <C>    <C>            <C>    <C>
Ratio of earnings to
  combined fixed charges
  and preference
  dividends.............    (a)     (a)    (a)    (a)   1.0x        (a)        (a)    (a)
</TABLE>
 
- ---------------
 
(a) Earnings were inadequate to cover combined fixed charges and preference
    dividends for the nine months ended September 30, 1998 and 1997 by
    $111,687,000 and $1,573,000, respectively, for the years ended December 31,
    1997 and 1996 by $9,322,000 and $7,260,000, respectively, for the seven
    months ended December 31, 1994 by $31,014,000 and for the years ended May
    31, 1994 and 1993 by $40,976,000 and $152,391,000, respectively. Without
    nonrecurring items, earnings would have been inadequate to cover combined
    fixed charges and preference dividends for the nine months ended September
    30, 1998 and 1997 by $34,022,000 and $7,826,000, respectively, for the years
    ended December 31, 1997 and 1995 by $15,175,000 and $10,723,000,
    respectively, for the seven months ended December 31, 1994 by $30,030,000,
    and for the years ended May 31, 1994 and 1993 by $51,415,000 and
    $45,183,000, respectively.
 
                                      S-12
<PAGE>   19
 
               PRICE RANGE OF ORDINARY SHARES AND DIVIDEND POLICY
 
TRADING PRICES
 
     Triton ordinary shares are listed on the New York Stock Exchange and are
traded under the symbol "OIL." Set forth below are the high and low closing
sales prices of Triton ordinary shares as reported on the New York Stock
Exchange Composite Tape for the periods indicated:
 
<TABLE>
<CAPTION>
                     CALENDAR PERIODS                        HIGH   LOW
<S>                                                          <C>    <C>
1998:
  First Quarter............................................  $36 3/4 $25 13/16
  Second Quarter...........................................   42 5/8  33 5/16
  Third Quarter............................................   36 3/4   9 15/16
  Fourth Quarter (through November 23).....................   12 7/16   8 1/2
1997:
  First Quarter............................................   52 1/2  38 1/4
  Second Quarter...........................................   45 13/16  32 3/8
  Third Quarter............................................   48     38 3/16
  Fourth Quarter...........................................   44 7/8  27 5/8
1996:
  First Quarter............................................   59 3/4  46 3/4
  Second Quarter...........................................   57 1/8  45 3/4
  Third Quarter............................................   49 3/8  40 1/2
  Fourth Quarter...........................................   50 5/8  42 1/2
</TABLE>
 
DIVIDEND POLICY
 
     Triton has not paid any dividends or distributions on its ordinary shares,
par value $.01 per share (the "Ordinary Shares"), since 1990. The holders of
Ordinary Shares are entitled to receive such dividends as are declared by the
Board of Directors. Triton's current intent, as to the Ordinary Shares, is to
retain earnings for use in Triton's business and the financing of its capital
requirements. The payment of any future cash dividends on the Ordinary Shares is
necessarily dependent upon the earnings and financial needs of Triton, along
with applicable legal and contractual restrictions. Triton is prohibited from
paying cash dividends on the Ordinary Shares under its credit facilities. In
addition, so long as HM4 Triton, L.P. and its affiliates own a certain number of
Ordinary Shares (assuming conversion of all 8% Preference Shares held by HM4
Triton, L.P. and its affiliates), Triton cannot pay a dividend on the Ordinary
Shares without HM4 Triton, L.P.'s consent. Finally, the terms of the 8%
Preference Shares and the 5% convertible preference shares prohibit the payment
of dividends on the Ordinary Shares unless full cumulative dividends on all such
outstanding preference shares have been paid in full or set aside for payment.
 
     The payment of dividends on the 8% Preference Shares may be made, at the
option of Triton, in cash or in additional 8% Preference Shares, subject to
certain conditions. See "Description of the 8% Preference Shares -- Dividends."
Triton does not know whether, as of any particular dividend payment period, it
will pay dividends in cash or in additional 8% Preference Shares. The payment of
any future cash dividends on the 8% Preference Shares is necessarily dependent
upon the earnings and financial needs of Triton, along with applicable legal and
contractual restrictions.
 
                                      S-13
<PAGE>   20
 
                                 CAPITALIZATION
 
     The following table sets forth the cash and equivalents and capitalization
of Triton and its consolidated subsidiaries at September 30, 1998 and as
adjusted to give effect to the issuance of the 8% Preference Shares and the
receipt of the proceeds from the sale thereof.
 
<TABLE>
<CAPTION>
                                                      AT SEPTEMBER 30, 1998
                                              --------------------------------------
                                               ACTUAL     ADJUSTMENTS    AS ADJUSTED
                                                          (IN THOUSANDS)
<S>                                           <C>         <C>            <C>
Cash and equivalents........................  $  59,332    $214,472(1)   $  263,871
                                              =========                  ==========
                                                             (9,933)(2)
                                                           ========
Debt:
  Short-term borrowings and current
     maturities of long-term debt...........  $  18,650    $ (9,623)(2)  $    9,027
  Long-term debt, excluding current
     maturities.............................    413,769        (310)(2)     413,459
                                              ---------    --------      ----------
          Total debt........................    432,419      (9,933)        422,486
Shareholders' equity:
  5% convertible preference shares, stated
     value $34.41...........................      7,214                       7,214
  8% Preference Shares, stated value $70....    127,575     222,425(3)      350,000
  Ordinary Shares, par value $.01...........        366                         366
  Additional paid-in capital................    580,117      (7,953)(4)     572,164
  Accumulated deficit.......................   (357,523)                   (357,523)
  Accumulated other non-owner changes in
     shareholders' equity...................     (2,126)                     (2,126)
                                              ---------    --------      ----------
                                                355,623     214,472         570,095
  Less cost of ordinary shares in
     treasury...............................          4                           4
                                              ---------    --------      ----------
          Total shareholders' equity........    355,619     214,472         570,091
                                              ---------    --------      ----------
          Total Capitalization..............  $ 788,038    $204,539      $  992,577
                                              =========    ========      ==========
</TABLE>
 
- -------------------------
 
(1) Adjustment represents proceeds from issuance of 3,177,500 8% Preference
    Shares at $70 per share, net of transaction costs of $5.6 million and a
    partial dividend payment of $2.4 million to HM4 Triton, L.P. See
    "Description of the 8% Preference Shares -- Dividends."
 
(2) Adjustment represents repayment of outstanding borrowings in October 1998
    with proceeds from the issuance in September 1998 of 1,822,500 8% Preference
    Shares to HM4 Triton, L.P. In November 1998, Triton borrowed $10 million
    under its credit facilities. A portion of the net proceeds from the sale of
    the 8% Preference Shares will be used to repay indebtedness outstanding
    under such credit facilities. Neither the incurrence of such debt nor its
    repayment is reflected above.
 
(3) Adjustment represents issuance of 3,177,500 8% Preference Shares at $70 per
    share.
 
(4) Adjustment represents estimated fees of $5.6 million associated with
    issuance of 8% Preference Shares, assuming HM4 Triton, L.P. acquires all
    shares, and a partial dividend payment of $2.4 million to HM4 Triton, L.P.
    See "Investment by Hicks Muse -- Payment of Expenses and Additional Fees"
    and "Description of the 8% Preference Shares -- Dividends."
 
                                      S-14
<PAGE>   21
 
                              THE RIGHTS OFFERING
 
THE RIGHTS
 
     Triton is distributing transferable rights (the "Rights") to the record
holders of its outstanding Ordinary Shares and 5% convertible preference shares,
par value $.01 per share ("5% Preference Shares"), as of November 30, 1998 (the
"Record Date"), at no cost to such record holders, and to the record holders, as
of the Record Date, of 8% Preference Shares pursuant to the Stock Purchase
Agreement between Triton and HM4 Triton, L.P., a Cayman Islands exempted limited
partnership ("HM4 Triton") and an affiliate of Hicks, Muse, Tate & Furst
Incorporated ("Hicks Muse"), dated August 31, 1998 (the "Stock Purchase
Agreement"). Triton will distribute .072 Rights for each Ordinary Share and each
5% Preference Share held of record on the Record Date. Triton will distribute
 .288 Rights for each 8% Preference Share held of record on the Record Date. One
Right plus $70 in cash (the "Subscription Price") will entitle the holder to
purchase one 8% Preference Share. The Rights will be evidenced by transferable
subscription certificates ("Subscription Certificates"). Approximately 3,177,500
Rights will be distributed in the Rights Offering.
 
     No fractional Rights or cash in lieu thereof will be issued or paid, and
the number of Rights distributed to each holder of Ordinary Shares, 5%
Preference Shares and 8% Preference Shares will be rounded up to the nearest
whole number of Rights. No Subscription Certificate may be divided in such a way
as to permit the holder of such Subscription Certificate to receive a greater
number of Rights than the number to which such Subscription Certificate entitles
its holder, except that brokers, dealers and other nominees holding Ordinary
Shares, 5% Preference Shares and 8% Preference Shares on the Record Date for
more than one beneficial owner will be able to obtain separate Subscription
Certificates for their beneficial owners so that they may each receive the
benefit of rounding. Triton reserves the right to refuse to issue any such
Subscription Certificate if such issuance would be inconsistent with the
principle that each beneficial owner's holdings will be rounded up to the
nearest whole Right.
 
     Because the number of Rights distributed to each record holder will be
rounded up to the nearest whole number, beneficial owners of Ordinary Shares, 5%
Preference Shares and 8% Preference Shares who are also the record holders of
such shares will receive more Rights under certain circumstances than beneficial
owners of such shares who are not the record holders of their shares and who do
not obtain (or cause the record holder of their shares to obtain) a separate
Subscription Certificate with respect to the Ordinary Shares, 5% Preference
Shares and 8% Preference Shares beneficially owned by them, including shares
held in an investment advisory or similar account. To the extent that record
holders or beneficial owners of Ordinary Shares, 5% Preference Shares and 8%
Preference Shares who obtain a separate Subscription Certificate receive more
Rights, they will be able to subscribe for more 8% Preference Shares.
 
SUBSCRIPTION PRIVILEGES
 
     Basic Subscription Privilege. One Right will entitle the holder thereof to
receive, upon payment of the Subscription Price, one 8% Preference Share (the
"Basic Subscription Privilege"). Certificates representing 8% Preference Shares
purchased pursuant to the
 
                                      S-15
<PAGE>   22
 
Basic Subscription Privilege will be delivered to subscribers as soon as
practicable after the Expiration Date (as defined herein), irrespective of
whether the Basic Subscription Privilege is exercised immediately prior to the
Expiration Date or earlier.
 
     Oversubscription Privilege. Subject to the allocation described below, each
Right also carries the right to subscribe at the Subscription Price for
additional 8% Preference Shares (the "Oversubscription Privilege") not
subscribed for through the exercise of the Basic Subscription Privilege by other
Rights holders (the "Excess Shares"). Only Rights holders who exercise the Basic
Subscription Privilege in full will be entitled to exercise the Oversubscription
Privilege. HM4 Triton has agreed not to exercise its Oversubscription Privilege.
 
     If the Excess Shares are not sufficient to satisfy all subscriptions
pursuant to the Oversubscription Privilege, the Excess Shares will be allocated
pro rata (subject to the elimination of fractional shares) among those Rights
holders exercising the Oversubscription Privilege in proportion, not to the
number of shares requested pursuant to the Oversubscription Privilege, but to
the number of Rights each beneficial holder exercised pursuant to the Basic
Subscription Privilege; provided, however, that if such pro rata allocation
results in any Rights holder being allocated a greater number of Excess Shares
than such holder subscribed for pursuant to the exercise of such holder's
Oversubscription Privilege, such holder will be allocated only such number of
Excess Shares as such holder subscribed for, and the remaining Excess Shares
will be allocated among all other holders exercising the Oversubscription
Privilege. Certificates representing Excess Shares purchased pursuant to the
Oversubscription Privilege will be delivered to subscribers as soon as
practicable after the Expiration Date and after all prorations and adjustments
contemplated by the terms of the Rights Offering have been effected.
 
     Banks, brokers and other nominee holders of Rights who exercise the Basic
Subscription Privilege and the Oversubscription Privilege on behalf of
beneficial owners of Rights will be required to certify to the Subscription
Agent and Triton, in connection with the exercise of the Oversubscription
Privilege, as to the aggregate number of Rights that have been exercised and the
number of 8% Preference Shares that are being subscribed for pursuant to the
Oversubscription Privilege by the beneficial owners of Rights on whose behalf
such nominee holder is acting.
 
EXPIRATION DATE
 
     The Rights will expire at 5:00 p.m., New York City time, on December 22,
1998 unless extended by Triton (the "Expiration Date"). After the Expiration
Date, unexercised Rights will be null and void. Triton will not be obligated to
honor any purported exercise of Rights received by the Subscription Agent after
the Expiration Date, regardless of when the documents relating to such exercise
were sent, except pursuant to the Guaranteed Delivery Procedures described
below.
 
DETERMINATION OF SUBSCRIPTION PRICE
 
     The $70 Subscription Price for the 8% Preference Shares was determined by
Triton through negotiations with HM4 Triton. On August 31, 1998, the date on
which Triton and HM4 Triton entered into the Stock Purchase Agreement, the
closing price of the Ordinary Shares was $12 1/8. As of November 23, 1998, the
closing price of the Ordinary Shares was
 
                                      S-16
<PAGE>   23
 
$10 3/16. Since the trading value of the 8% Preference Shares will most likely
be based on the market price of the underlying Ordinary Shares and the value
given to the dividend rights and other preferences of the 8% Preference Shares,
if the market price of the Ordinary Shares does not increase, the 8% Preference
Shares will most likely trade at a price that is less than the $70 per share
Subscription Price, if they trade at all.
 
     There is currently no public market for the 8% Preference Shares. The 8%
Preference Shares have been approved for listing on the New York Stock Exchange,
but the approval is subject to satisfaction of certain minimum distribution
requirements which require that there be at least 100 beneficial holders of
100,000 publicly held 8% Preference Shares with an aggregate market value of at
least $2 million. Shares held by HM4 Triton do not count for purposes of this
calculation. The market price for the Ordinary Shares is currently significantly
below the conversion price of the 8% Preference Shares. Therefore, there is a
substantial risk that an insufficient number of holders will exercise their
Rights and the distribution requirements will not be satisfied. Even if the 8%
Preference Shares are listed on the New York Stock Exchange, Triton does not
know the extent to which a public market for the shares will develop, how liquid
any market may be or the price at which the 8% Preference Shares may trade.
 
     There can be no assurance that the market price of the Ordinary Shares will
not decline during the subscription period or that, following the issuance of
the Rights and of the 8% Preference Shares upon exercise of Rights, a
subscribing Rights holder will be able to sell 8% Preference Shares purchased in
the Rights Offering at a price equal to or greater than the Subscription Price.
See "Risk Factors -- Market Considerations."
 
EXERCISE OF RIGHTS
 
     Rights may be exercised by delivery to ChaseMellon Shareholder Services,
L.L.C., as subscription agent (the "Subscription Agent"), on or prior to the
Expiration Date, of the properly completed and duly executed Subscription
Certificate evidencing such Rights (together with any required signature
guarantees), accompanied by payment in full of the Subscription Price for each
8% Preference Share subscribed for pursuant to the Basic Subscription Privilege
and the Oversubscription Privilege (except as permitted pursuant to clause (iii)
of the next sentence). Such payment in full must be made by (i) check or bank
draft drawn upon a United States bank or postal, telegraphic or express money
order payable to ChaseMellon Shareholder Services, L.L.C., as Subscription
Agent; (ii) wire transfer of funds to the account maintained by the Subscription
Agent for such purpose at The Chase Manhattan Bank, New York, NY, ABA No.
021000021 -- Attn: ChaseMellon Shareholder Services Reorg. Account: 323-859577
(Triton Energy Limited); or (iii) in such other manner as Triton may approve in
writing in the case of persons acquiring 8% Preference Shares at an aggregate
Subscription Price of $1.5 million or more, provided that in such case the full
amount of such Subscription Price is received by the Subscription Agent in
currently available funds within three New York Stock Exchange trading days
following the Expiration Date (the payment method under clause (iii) being an
"Approved Payment Method"). Payment of the Subscription Price will be deemed to
have been received by the Subscription Agent only upon (a) clearance of any
uncertified check, (b) receipt by the Subscription Agent of any certified check
or bank draft drawn upon a U.S. bank or of any postal, telegraphic or express
money order, (c) receipt of good funds in the Subscription Agent's account
designated above or (d) receipt of funds by the
 
                                      S-17
<PAGE>   24
 
Subscription Agent through an Approved Payment Method. PLEASE NOTE THAT FUNDS
PAID BY UNCERTIFIED PERSONAL CHECK MAY TAKE AT LEAST FIVE BUSINESS DAYS TO
CLEAR. ACCORDINGLY, HOLDERS WHO WISH TO PAY THE SUBSCRIPTION PRICE BY MEANS OF
UNCERTIFIED PERSONAL CHECK ARE URGED TO MAKE PAYMENT SUFFICIENTLY IN ADVANCE OF
THE EXPIRATION DATE TO ENSURE THAT SUCH PAYMENT IS RECEIVED AND CLEARS BY SUCH
DATE, AND ARE URGED TO CONSIDER PAYMENT BY MEANS OF CERTIFIED OR CASHIER'S
CHECK, MONEY ORDER OR WIRE TRANSFER OF FUNDS.
 
     Subscription Certificates and payment of the Subscription Price should be
delivered to one of the addresses set forth below under "-- Subscription Agent."
 
     If a Rights holder wishes to exercise Rights, but time will not permit such
holder to cause the Subscription Certificate(s) evidencing such Rights to reach
the Subscription Agent on or prior to the Expiration Date, such Rights may
nevertheless be exercised if all of the following conditions (the "Guaranteed
Delivery Procedures") are met:
 
          (i) such holder has caused payment in full of the Subscription Price
     for each 8% Preference Share being subscribed for pursuant to the Basic
     Subscription Privilege and the Oversubscription Privilege to be received
     (in the manner set forth above) by the Subscription Agent on or prior to
     the Expiration Date;
 
          (ii) the Subscription Agent receives, on or prior to the Expiration
     Date, a notice of guaranteed delivery (a "Notice of Guaranteed Delivery"),
     substantially in the form provided with the Instructions as to Use of
     Triton Energy Limited Subscription Certificates (the "Instructions")
     distributed with the Subscription Certificates, from a member firm of a
     registered national securities exchange or a member of the National
     Association of Securities Dealers, Inc., or from a commercial bank or trust
     company having an office or correspondent in the United States, stating the
     name of the exercising Rights holder, the number of Rights represented by
     the Subscription Certificate(s) held by such exercising holder, the number
     of 8% Preference Shares being subscribed for pursuant to the Basic
     Subscription Privilege and the number of shares, if any, being subscribed
     for pursuant to the Oversubscription Privilege, and guaranteeing the
     delivery to the Subscription Agent of any Subscription Certificate(s)
     evidencing such Rights within three New York Stock Exchange trading days
     following the date of the Notice of Guaranteed Delivery; and
 
          (iii) the properly completed and duly executed Subscription
     Certificate(s), including any required signature guarantees, evidencing the
     Rights being exercised is received by the Subscription Agent within three
     New York Stock Exchange trading days following the date of the Notice of
     Guaranteed Delivery relating thereto. The Notice of Guaranteed Delivery may
     be delivered to the Subscription Agent in the same manner as Subscription
     Certificates at the addresses set forth below, or may be transmitted to the
     Subscription Agent by facsimile transmission (facsimile no. (201)
     296-4293). Additional copies of the form of Notice of Guaranteed Delivery
     are available upon request from ChaseMellon Shareholder Services, L.L.C.,
     in its capacity as information agent (the "Information Agent").
 
     Unless a Subscription Certificate (i) provides that the 8% Preference
Shares to be issued pursuant to the exercise of Rights represented thereby are
to be delivered to the
 
                                      S-18
<PAGE>   25
 
record holder of such Rights or (ii) is submitted for the account of bank or
broker, signatures on such Subscription Certificate must be guaranteed by an
eligible guarantor institution ("Eligible Guarantor Institution") as defined in
Rule 17Ad-15 of the Exchange Act, subject to the standards and procedures
adopted by the Subscription Agent.
 
     Funds received in payment of the Subscription Price for Excess Shares
subscribed for pursuant to the Oversubscription Privilege will be held in a
segregated account pending issuance of such Excess Shares. If a Rights holder
exercising the Oversubscription Privilege is allocated fewer than all of the
Excess Shares that such holder wished to subscribe for pursuant to the
Oversubscription Privilege, the excess funds paid by such holder in respect of
the Subscription Price for shares not issued will be returned by mail, without
interest or deduction, as soon as practicable after the Expiration Date.
 
     A holder of record who holds Ordinary Shares, 5% Preference Shares or 8%
Preference Shares for the account of others, such as a broker, a trustee or a
depository for securities, should notify the respective beneficial owners of
such shares as soon as possible to ascertain such beneficial owners' intentions
and to obtain instructions with respect to the Rights beneficially owned by
them. Beneficial owners of Ordinary Shares, 5% Preference Shares, 8% Preference
Shares or Rights held through such a holder of record should contact the holder
and request the holder to effect transactions in accordance with the beneficial
owners' instructions.
 
     If either the number of Rights being exercised is not specified on a
Subscription Certificate, or the payment delivered is not sufficient to pay the
full aggregate Subscription Price for all shares of 8% Preference Shares stated
to be subscribed for, the Rights holder will be deemed to have exercised the
maximum number of Rights that could be exercised for the amount of the payment
delivered by such Rights holder. If the payment delivered by the Rights holder
exceeds the aggregate Subscription Price for the number of Rights evidenced by
the Subscription Certificate(s) delivered by such Rights holder, the payment
will be applied, until depleted, to subscribe for 8% Preference Shares in the
following order: (i) to subscribe for the number of shares, if any, of 8%
Preference Shares indicated on the Subscription Certificate(s) pursuant to the
Basic Subscription Privilege; (ii) to subscribe for 8% Preference Shares until
the Basic Subscription Privilege has been fully exercised with respect to all of
the Rights represented by the Subscription Certificate; and (iii) to subscribe
for additional shares of 8% Preference Shares pursuant to the Oversubscription
Privilege (subject to any applicable proration). Any excess payment remaining
after the foregoing allocation will be returned to the Rights holder by mail,
without interest or deduction, as soon as practicable after the Expiration Date.
 
     The Instructions accompanying the Subscription Certificates should be read
carefully and followed in detail. DO NOT SEND SUBSCRIPTION CERTIFICATES TO
TRITON. THE METHOD OF DELIVERY OF SUBSCRIPTION CERTIFICATES AND PAYMENT OF THE
SUBSCRIPTION PRICE TO THE SUBSCRIPTION AGENT WILL BE AT THE ELECTION AND RISK OF
THE RIGHTS HOLDERS, BUT IF SENT BY MAIL IT IS RECOMMENDED THAT SUCH CERTIFICATES
AND PAYMENTS BE SENT BY REGISTERED MAIL, PROPERLY INSURED, WITH RETURN RECEIPT
REQUESTED, AND THAT A SUFFICIENT NUMBER OF DAYS BE ALLOWED TO ENSURE DELIVERY TO
THE SUBSCRIPTION AGENT AND CLEARANCE OF PAYMENT PRIOR TO THE EXPIRATION DATE.
BECAUSE UNCERTIFIED PERSONAL CHECKS MAY TAKE AT LEAST
 
                                      S-19
<PAGE>   26
 
FIVE BUSINESS DAYS TO CLEAR, RIGHTS HOLDERS ARE STRONGLY URGED TO PAY, OR
ARRANGE FOR PAYMENT, BY MEANS OF CERTIFIED OR CASHIER'S CHECK, MONEY ORDER OR
WIRE TRANSFER OF FUNDS.
 
     All questions concerning the timeliness, validity, form and eligibility of
any exercise of Rights will be determined by the Subscription Agent, in
consultation with Triton, whose determinations will be final and binding.
Triton, in its sole discretion, may waive any defect or irregularity, or permit
a defect or irregularity to be corrected within such time as it may determine,
or reject the purported exercise of any Right by reason of any defect or
irregularity in such exercise. Subscriptions will not be deemed to have been
received or accepted until all irregularities have been waived or cured within
such time as Triton determines in its sole discretion. Neither Triton nor the
Subscription Agent will be under any duty to give notification of any defect or
irregularity in connection with the submission of Subscription Certificates or
incur any liability for failure to give such notification.
 
     Any questions or requests for assistance concerning the method of
exercising Rights or requests for additional copies of this Prospectus
Supplement, together with the accompanying Prospectus, the Instructions or the
Notice of Guaranteed Delivery should be directed to the Dealer Manager,
Donaldson, Lufkin & Jenrette Securities Corporation, or to the Information
Agent, ChaseMellon Shareholder Services, L.L.C., at their respective addresses
set forth on the back cover page of this Prospectus Supplement.
 
NO REVOCATION
 
     AFTER A HOLDER OF RIGHTS HAS EXERCISED THE BASIC SUBSCRIPTION PRIVILEGE OR
THE OVERSUBSCRIPTION PRIVILEGE, SUCH EXERCISE MAY NOT BE REVOKED BY SUCH RIGHTS
HOLDER.
 
METHOD OF TRANSFERRING RIGHTS
 
     Rights may be purchased or sold through usual investment channels,
including banks and brokers. The Rights will be eligible to trade on the New
York Stock Exchange until the close of business on the last New York Stock
Exchange trading day preceding the Expiration Date. Triton does not know the
extent to which investor interest will lead to the development of a trading
market for the Rights, how liquid any market might be, how long any market might
last or the price at which the Rights may trade. See "Risk Factors -- Market
Considerations."
 
     Rights evidenced by a single Subscription Certificate may be transferred in
whole by endorsing the Subscription Certificate for transfer in accordance with
the Instructions. A portion of the Rights evidenced by a single Subscription
Certificate (but not fractional Rights) may be transferred by delivering to the
Subscription Agent a Subscription Certificate properly endorsed for transfer,
with instructions to register such portion of the Rights evidenced thereby in
the name of the transferee (and to issue a new Subscription Certificate to the
transferee evidencing such transferred Rights). In such event, a new
Subscription Certificate evidencing the balance of the Rights will be issued to
the Rights holder or, if the holder so instructs, to an additional transferee.
 
     Rights holders wishing to transfer a portion of their Rights (but not
fractional Rights) should allow a sufficient amount of time prior to the
Expiration Date for (i) the transfer
 
                                      S-20
<PAGE>   27
 
instructions to be received and processed by the Subscription Agent, (ii) a new
Subscription Certificate to be issued and transmitted to the transferee or
transferees with respect to transferred Rights, and to the transferor with
respect to retained Rights, if any, and (iii) the Rights evidenced by such new
Subscription Certificates to be exercised or sold by the recipients thereof.
Neither Triton nor the Subscription Agent will have any liability to a
transferee or transferor of Rights if Subscription Certificates are not received
in time for exercise or sale prior to the Expiration Date.
 
     Except for the fees charged by the Subscription Agent (which will be paid
by Triton as described herein), all commissions, fees and other expenses
(including brokerage commissions and transfer taxes) incurred in connection with
the purchase, sale or exercise of Rights will be for the account of the
transferor of the Rights, and none of such commissions, fees or expenses will be
paid by Triton or the Subscription Agent.
 
PROCEDURES FOR BOOK ENTRY TRANSFER FACILITY PARTICIPANTS
 
     Triton anticipates that the Rights will be eligible for transfer through,
and that the exercise of the Basic Subscription Privilege may be effected
through, the facilities of Depository Trust Company ("DTC"). Rights exercised
through DTC are referred to herein as "DTC Exercised Rights." The holder of a
DTC Exercised Right may exercise the Oversubscription Privilege in respect of
such DTC Exercised Right by properly executing and delivering to the
Subscription Agent on or prior to the Expiration Date, a DTC Participant
Oversubscription Exercise Form, together with payment of the appropriate
Subscription Price for the number of 8% Preference Shares for which the
Oversubscription Privilege is to be exercised. Copies of the DTC Participant
Oversubscription Exercise Form may be obtained from the Dealer Manager or the
Information Agent.
 
NON-U.S. AND CERTAIN OTHER SHAREHOLDERS
 
     Subscription Certificates will not be mailed to Rights holders or to any
subsequent transferees of any Subscription Certificates whose addresses are
outside the United States or who have APO or FPO addresses, but will be held by
the Subscription Agent for such holders' accounts. To exercise or sell their
Rights, such holders must notify the Subscription Agent prior to 11:00 a.m., New
York City time, at least three New York Stock Exchange trading days prior to the
Expiration Date, at which time (if no contrary instructions have been received)
the Rights represented thereby will be sold, subject to the Subscription Agent's
ability to find a purchaser. Any such sales will be at prevailing market prices.
See "Risk Factors -- Market Considerations." If the Rights can be sold, a check
for the proceeds from the sale of any Rights, less any applicable brokerage
commissions, taxes and other expenses, will be remitted, without interest, to
such holders by mail. The proceeds, if any, resulting from sales of Rights of
holders whose addresses are not known by the Subscription Agent or to whom
delivery cannot be made will be held by the Subscription Agent in a noninterest
bearing account. Any amount remaining unclaimed on the second anniversary of the
Expiration Date will be turned over by the Subscription Agent to Triton and,
after such date, any person claiming such proceeds will, as an unsecured general
creditor of Triton, be entitled to look only to Triton for payment thereof. The
ability of such holders to exercise or sell Rights will expire on the Expiration
Date.
 
                                      S-21
<PAGE>   28
 
SUBSCRIPTION AGENT
 
     Triton has appointed ChaseMellon Shareholder Services, L.L.C. as
Subscription Agent for the Rights Offering. The Subscription Agent's address,
which is the address to which the Subscription Certificates and payment of the
Subscription Price should be delivered, as well as the address to which Notice
of Guaranteed Delivery must be delivered, is:
 
     By Mail:
 
            ChaseMellon Shareholder Services, L.L.C.
            Post Office Box 3301
            South Hackensack, NJ 07606
            Attn: Reorganization Department
 
     By Hand:
 
            ChaseMellon Shareholder Services, L.L.C.
            120 Broadway, 13th Floor
            New York, NY 10271
            Attn: Reorganization Department
 
     By Overnight Delivery:
 
            ChaseMellon Shareholder Services, L.L.C.
            85 Challenger Road -- Mail Drop Reorg.
            Ridgefield Park, NJ 07660
            Attn: Reorganization Department
 
     The Subscription Agent's toll-free telephone number is (877) 698-6867, and
its facsimile number is (201) 296-4293 (confirmation number (201) 296-4860).
 
     Triton will pay the fees and expenses of the Subscription Agent and has
also agreed to indemnify the Subscription Agent from any liability which it may
incur in connection with the Rights Offering.
 
INFORMATION AGENT
 
     Triton has appointed ChaseMellon Shareholder Services, L.L.C. as
Information Agent for the Rights Offering. Any questions or requests for
additional copies of this Prospectus Supplement, together with the accompanying
Prospectus, the Instructions or the Notice of Guaranteed Delivery may be
directed to the Information Agent at the following address and telephone number:
 
            ChaseMellon Shareholder Services, L.L.C.
            450 West 33rd Street, 14th Floor
            New York, NY 10001
 
            Banks and brokers call collect: (212) 273-8070
            All others call toll-free: (877) 698-6867
 
     Triton will pay the fees and expenses of the Information Agent and has also
agreed to indemnify the Information Agent from certain liabilities that it may
incur in connection with the Rights Offering.
                                      S-22
<PAGE>   29
 
DEALER MANAGER
 
     The 8% Preference Shares offered pursuant to the Rights Offering are being
offered by Triton directly to the holders of Ordinary Shares, 5% Preference
Shares and 8% Preference Shares. Triton has appointed Donaldson, Lufkin &
Jenrette Securities Corporation as Dealer Manager for the Rights Offering. The
Dealer Manager will communicate with brokers, dealers, commercial banks and
trust companies with respect to the Rights Offering and respond to requests for
information and material in connection with the Rights Offering. Triton has
agreed to pay Donaldson, Lufkin & Jenrette Securities Corporation a customary
fee for acting as Dealer Manager and to reimburse certain of the Dealer
Manager's expenses. The Dealer Manager is not required to purchase Rights or 8%
Preference Shares in connection with the Rights Offering.
 
     The Dealer Manager may be deemed to be an underwriter under the Securities
Act, and, therefore, the fee to be paid to the Dealer Manager may be deemed to
be underwriting fees and commissions. Triton has agreed to indemnify the Dealer
Manager against certain liabilities, including civil liabilities under the
Securities Act, or to contribute to payments which the Dealer Manager may be
required to make in respect thereof.
 
     Other than the arrangements with the Dealer Manager described above, Triton
has not employed any brokers, dealers or underwriters in connection with the
solicitation of exercises of Rights in the Rights Offering, and, except as
described above, no other commissions, fees or discounts will be paid in
connection with the Rights Offering. Certain employees of Triton may solicit
responses from shareholders and Rights holders, but such employees will not
receive any commissions or compensation for such services other than their
normal employment compensation.
 
                                      S-23
<PAGE>   30
 
                            INVESTMENT BY HICKS MUSE
 
     The following statements with respect to the Stock Purchase Agreement, the
Financial Advisory Agreement, the Monitoring Agreement and the Shareholders
Agreement (each as defined herein) are subject to the detailed provisions of
such agreements which have been filed as exhibits to documents incorporated by
reference herein. See "Available Information" and "Incorporation of Certain
Documents by Reference" in the Prospectus accompanying this Prospectus
Supplement. The following statements do not purport to be complete, and while
Triton believes the descriptions of the material provisions of these agreements
contained herein are accurate statements with respect to such material
provisions, such statements are subject to the detailed provisions of such
agreements, to which reference is hereby made for a full description of such
provisions.
 
PURCHASE AND SALE OF 8% PREFERENCE SHARES
 
     On August 31, 1998, Triton entered into a stock purchase agreement (the
"Stock Purchase Agreement") which provides for the issuance and sale by Triton
to HM4 Triton of 8% Preference Shares as follows:
 
          (a) At the closing of the initial purchase of 8% Preference Shares by
     HM4 Triton, which occurred on September 30, 1998 (the "First Closing"),
     Triton issued and sold to HM4 Triton 1,822,500 8% Preference Shares at a
     purchase price of $70 per share (or an aggregate purchase price of
     $127,575,000).
 
          (b) At the closing of the purchase of 8% Preference Shares following
     the completion of the Rights Offering (the "Second Closing"), subject to
     the satisfaction of the conditions described below, Triton will issue and
     sell to HM4 Triton an additional number of 8% Preference Shares equal to
     the sum of (i) 524,800 8% Preference Shares upon exercise of the Rights
     distributed to HM4 Triton in the Rights Offering with respect to its 8%
     Preference Shares and (ii) all 8% Preference Shares which are unsubscribed
     for upon termination of the Rights Offering; provided that the number of 8%
     Preference Shares purchased by HM4 Triton at the Second Closing will not be
     greater than 3,177,500.
 
CONDITIONS TO SECOND CLOSING
 
     The obligations of Triton and HM4 Triton to consummate the transactions at
the Second Closing are subject to the satisfaction or waiver of certain
conditions, including (i) that the representations and warranties of each party
contained in the Stock Purchase Agreement are true and correct as of the Second
Closing except for failures which, individually or in the aggregate, have not
had and could not reasonably be expected to have a material adverse effect on
Triton, (ii) that each party will have performed all obligations required to be
performed by it under the Stock Purchase Agreement except for failures to be
true and correct which, individually or in the aggregate, have not had and could
not reasonably be expected to have a material adverse effect on Triton, (iii)
that the Rights Offering will have commenced, the time periods for the Basic
Subscription Privilege and the Oversubscription Privilege will have expired and
the number of Excess Shares will have been determined and (iv) that members of
Triton's Board of Directors designated by HM4 Triton pursuant to the
Shareholders Agreement will not have been removed (other than at the direction
of HM4 Triton). The satisfaction of the conditions to HM4 Triton's
 
                                      S-24
<PAGE>   31
 
obligations is not a condition to the consummation of the Rights Offering or to
the obligations of any holder (other than HM4 Triton) to purchase 8% Preference
Shares subscribed for. All holders other than HM4 Triton will be required to
purchase any 8% Preference Shares subscribed for regardless of whether such
conditions are satisfied.
 
TERMINATION
 
     The Stock Purchase Agreement can be terminated under a number of
circumstances, including, among others, the following: (i) by mutual consent of
Triton and HM4 Triton; (ii) by either party if the other party has breached its
representations, warranties or covenants and such breach is not cured promptly
pursuant to the Stock Purchase Agreement and prevents satisfaction of the
conditions to the Second Closing; (iii) by either party if the Second Closing
does not occur before the later of (A) January 4, 1999, and (B) the date to
which the Second Closing is extended as permitted under the Stock Purchase
Agreement; (iv) by Triton if the Board of Directors of Triton has determined in
good faith, based upon advice of counsel, that it is necessary to terminate the
Stock Purchase Agreement and to enter into an agreement with respect to any Sale
Transaction as described below in order to comply with its fiduciary duties; (v)
by HM4 Triton if the Board of Triton has recommended, resolved to recommend, or
failed to recommend against certain competing business combinations or change of
control transactions involving Triton; or (vi) by either party if a court of
competent jurisdiction has issued a final order, decree or ruling prohibiting
the transactions contemplated by the Stock Purchase Agreement.
 
     If Triton terminates the Stock Purchase Agreement pursuant to clause (iv)
above, Triton must pay a $30 million fee to HM4 Triton. Subject to certain
exceptions, if the Stock Purchase Agreement is terminated for any other reason
(other than by mutual consent of Triton and HM4 Triton) and within one year
after such termination Triton enters into a definitive agreement with respect to
(and thereafter consummates) a Sale Transaction (as defined below) or 50% or
more of the outstanding Ordinary Shares or voting securities representing 50% or
more of the voting power of Triton's outstanding capital stock (assuming the
conversion of the 8% Preference Shares) are acquired in a tender or exchange
offer in connection with a Sale Transaction or in such a tender or exchange
offer that was commenced but did not expire during such one-year period and
which is subsequently consummated, Triton must pay a $30 million termination fee
to HM4 Triton.
 
PAYMENT OF EXPENSES AND ADDITIONAL FEES
 
     The Stock Purchase Agreement requires Triton to reimburse HM4 Triton for
its reasonable out-of-pocket fees, costs and expenses incurred in connection
with the Stock Purchase Agreement (including fees and expenses of accountants,
counsel, financial advisors and other similar advisors).
 
     Pursuant to a Financial Advisory Agreement (the "Financial Advisory
Agreement") between Triton and Hicks, Muse & Co. Partners, L.P., an affiliate of
Hicks Muse ("Hicks Muse Partners"), entered into in connection with the Stock
Purchase Agreement, Triton paid Hicks Muse Partners a transaction fee of
$9,551,500 at the First Closing, and Triton is required to pay to Hicks Muse
Partners a transaction fee equal to 2% of the purchase price for the 8%
Preference Shares purchased by HM4 Triton at the Second Closing, in
 
                                      S-25
<PAGE>   32
 
each case, for services as financial advisor to Triton in connection with the
transactions contemplated by the Stock Purchase Agreement. In accordance with
the terms of the Financial Advisory Agreement, Triton has retained Hicks Muse
Partners as its exclusive financial advisor in connection with any Sale
Transaction described below unless Hicks Muse Partners and Triton mutually agree
to retain an additional financial advisor in connection with any particular Sale
Transaction. The Financial Advisory Agreement requires Triton to pay a fee to
Hicks Muse Partners in connection with any Sale Transaction (unless the Chief
Executive Officer of Triton elects not to retain a financial advisor) in an
amount equal to the lesser of (i) the amount of fees then charged by first-tier
investment banking firms for similar advisory services rendered in similar
transactions or (ii) 1.5% of the Transaction Value (as defined in the Financial
Advisory Agreement); provided that (A) such fee will be divided equally between
Hicks Muse Partners and any additional financial advisor which Triton and Hicks
Muse Partners agree will be retained by Triton with respect to any such
transaction and (B) Hicks Muse Partners will not be entitled to a fee with
respect to any such transaction for which the Chief Executive Officer of Triton
elects not to retain a financial advisor. "Sale Transaction" is defined in the
Financial Advisory Agreement as any merger, consolidation, sale of securities
representing a majority of the combined voting power of Triton, sale of assets
of Triton representing more than 50% of the total market value of the assets of
Triton and its subsidiaries or other similar transaction. Triton is also
required to reimburse Hicks Muse Partners for reasonable disbursements and
out-of-pocket expenses of Hicks Muse Partners incurred in connection with its
advisory services. The Financial Advisory Agreement will remain in effect until
the earlier of (i) August 31, 2008 or (ii) the date on which HM4 Triton and its
affiliates cease to own beneficially, directly or indirectly, at least 5% of
Triton's outstanding Ordinary Shares (determined after giving effect to the
conversion of all 8% Preference Shares held by HM4 Triton and its affiliates).
Triton has agreed to indemnify Hicks Muse Partners with respect to liabilities
incurred as a result of Hicks Muse Partners' performance of services for Triton
pursuant to the Financial Advisory Agreement.
 
     Pursuant to the Stock Purchase Agreement, Triton and Hicks Muse Partners
also entered into a Monitoring and Oversight Agreement (the "Monitoring
Agreement") under which Hicks Muse Partners will provide financial oversight and
monitoring services as requested by Triton and Triton will pay to Hicks Muse
Partners an annual fee of $500,000. In addition, Triton will reimburse Hicks
Muse Partners for reasonable disbursements and out-of-pocket expenses incurred
by Hicks Muse Partners or its affiliates for the account of Triton or in
connection with the performance of its services. The Monitoring Agreement will
remain in effect until the earlier of (i) September 30, 2008 or (ii) the date on
which HM4 Triton and its affiliates cease to own beneficially, directly or
indirectly, at least 5% of Triton's outstanding Ordinary Shares (determined
after giving effect to the conversion of all 8% Preference Shares held by HM4
Triton and its affiliates). Triton has agreed to indemnify Hicks Muse Partners
with respect to liabilities incurred as a result of Hicks Muse Partners'
performance of services for Triton pursuant to the Monitoring Agreement.
 
INDEMNIFICATION OF DIRECTORS AND OFFICERS
 
     As required by the Stock Purchase Agreement, Triton obtained directors' and
officers' liability insurance policies providing an aggregate of $25 million in
additional coverage (the "Additional D&O Policies") to the coverage provided by
Triton's previously existing directors' and officers' insurance policy. In
addition, the Stock Purchase Agreement
 
                                      S-26
<PAGE>   33
 
requires Triton to use its commercially reasonable efforts to obtain insurance
coverage for HM4 Triton and any of its affiliates with respect to any claims
arising out of any act or omission of any director of Triton in his or her
capacity as a director of Triton. Triton is required to maintain the foregoing
policies for so long as HM4 Triton is entitled to nominate members of the Board
of Directors of Triton. See "-- The Shareholders Agreement -- Board
Composition."
 
     In addition, until the later of (i) September 30, 2002 or (ii) the final
resolution of certain shareholder class action proceedings against Triton, the
Stock Purchase Agreement requires that Triton maintain in effect its current
directors' and officers' liability insurance policies (or Triton may substitute
policies of no less favorable terms and amounts) with respect to matters
occurring prior to the Second Closing, provided that Triton is not required to
spend more than 150% of the current annual premiums paid by Triton for such
insurance per year.
 
INDEMNIFICATION OF HM4 TRITON AND TRITON
 
     The representations and warranties and the covenants contained in the Stock
Purchase Agreement or any other transaction agreement that are required to be
performed or complied with on or prior to either the First Closing or the Second
Closing survive until the first anniversary of the Second Closing. Covenants
required to be performed or complied with following either the First Closing or
the Second Closing will survive until the later of (i) the first anniversary of
the Second Closing or (ii) expiration of the applicable statute of limitations.
The Stock Purchase Agreement contains certain mutual indemnification agreements
between HM4 Triton and Triton for liabilities arising out of breaches of
representations, warranties, covenants and agreements contained in the Stock
Purchase Agreement, the Shareholders Agreement or the 8% Preference Shares
Authorization (as defined herein) or (in the case of claims or liabilities
incurred by HM4 Triton) arising out of any shareholder litigation with respect
to the transactions contemplated by the Stock Purchase Agreement, the
Shareholders Agreement or the 8% Preference Shares Authorization; provided that
claims for indemnity with respect to the breach of representations and
warranties generally are not required to be paid by either party unless the
aggregate amount of all such claims payable by such party equals or exceeds $2.5
million, and then only to the extent of the amount in excess of $2.5 million;
provided, further, that any claim must be brought within the applicable survival
period. Triton's indemnification obligations are limited to the aggregate
purchase price paid by HM4 Triton at the First Closing and the Second Closing.
 
AMENDMENT TO SHAREHOLDER RIGHTS PLAN
 
     In connection with the Stock Purchase Agreement, Triton amended the
Shareholder Rights Plan previously adopted by the Board of Directors of Triton
to allow HM4 Triton to become the beneficial owner of 15% or more of the
outstanding Ordinary Shares, including by the acquisition of 8% Preference
Shares at the First Closing and the Second Closing, without triggering a
distribution of the preference share purchase rights under the Shareholder
Rights Plan. However, HM4 Triton will cease to be exempt from the provisions of
the Shareholder Rights Plan triggering such a distribution when HM4 Triton
ceases to own Ordinary Shares and 8% Preference Shares (assuming conversion of
such shares held by HM4 Triton and its affiliates into Ordinary Shares)
representing at least
 
                                      S-27
<PAGE>   34
 
(i) 50% of the Original Number (as defined herein) or (ii) 10% of the
outstanding Ordinary Shares (assuming the conversion or exchange of all
outstanding convertible or exchangeable securities of Triton).
 
THE SHAREHOLDERS AGREEMENT
 
     At the First Closing, Triton and HM4 Triton entered into a Shareholders
Agreement (the "Shareholders Agreement") relating to the 8% Preference Shares
and Ordinary Shares owned by HM4 Triton from time to time and certain other
corporate matters. The provisions of the Shareholders Agreement remain in effect
until September 30, 2008, except where otherwise noted.
 
     Board Composition. The Shareholders Agreement provides that, subject to the
following paragraph, so long as the entire Board of Directors of Triton (the
"Board") consists of ten members, HM4 Triton (and its designated transferees,
collectively) may designate four nominees for election to the Board (with such
number of designees increasing or decreasing proportionately with any change in
the total number of members of the Board and with any fractional directorship
resulting from such calculation being rounded up to the next whole number).
Triton and the Board are obligated to cause HM4 Triton's designees to be
nominated for election to the Board. Following the First Closing, HM4 Triton
designated four nominees to the Board who were appointed by the Board to fill
existing vacancies.
 
     The right of HM4 Triton (and its designated transferees) to designate
nominees for election to the Board will be reduced if, at any time after the
Second Closing, the number of Ordinary Shares and 8% Preference Shares (assuming
conversion of such shares into Ordinary Shares) held of record by HM4 Triton and
its affiliates (the "HM4 Record Ownership") represents less than certain
specified percentages of the number of shares of Ordinary Shares into which the
total number of 8% Preference Shares purchased by HM4 Triton pursuant to the
Stock Purchase Agreement (including 8% Preference Shares purchased pursuant to
the exercise of the Rights) are convertible (the "Original Number").
Specifically, if the HM4 Record Ownership is less than 75% but equal to or more
than 50% of the Original Number, HM4 Triton will be entitled to designate three
nominees, if the HM4 Record Ownership is less than 50% but equal to or more than
25% of the Original Number, HM4 will be entitled to designate two nominees, if
the HM4 Record Ownership is less than 25% but equal to or more than 1% of the
Original Number, HM4 Triton will be entitled to designate one nominee and if the
HM4 Record Ownership is less than 1% of the Original Number, HM4 Triton will not
be entitled to designate any nominees. In addition, in any period in which HM4
Triton (and its designated transferees) holds a majority of the outstanding 8%
Preference Shares and the holders of the 8% Preference Shares, voting separately
as a class, are entitled to elect two directors of Triton due to dividend
arrearages, the number of nominees that HM4 Triton may designate will be reduced
so that such nominees and the two directors elected by the holders of the 8%
Preference Shares together constitute less than 50% of the Board. See
"Description of the 8% Preference Shares -- Voting."
 
     Board Committees. So long as HM4 Triton is entitled to designate one
nominee for director, Triton and the Board are required to cause at least one
HM4 Triton director to be elected to, and at all times to be a member of, each
committee of the Board.
 
                                      S-28
<PAGE>   35
 
     Restrictions on Transfer. Under the Shareholders Agreement, without the
consent of Triton, HM4 Triton may not, during the one-year period following the
First Closing, sell or otherwise transfer any 8% Preference Shares or Ordinary
Shares held by it (including Ordinary Shares issued upon conversion of the 8%
Preference Shares), other than pursuant to certain permitted transfers,
including, among others, transfers to affiliates, transfers pursuant to a
registered public offering or Rule 144 offering under the Securities Act or
pursuant to a tender or exchange offer for all of the Ordinary Shares. Until the
earlier of the fifth anniversary of the First Closing or the date on which HM4
Triton and its affiliates own less than 10% of the then outstanding Ordinary
Shares (assuming conversion of all convertible shares, including the 8%
Preference Shares, then held by HM4 Triton and its affiliates), Triton will have
a right of first offer (or to obtain a third-party buyer) with respect to any
sale other than any permitted transfer by HM4 Triton or its affiliates, of 8%
Preference Shares and/or Ordinary Shares representing, in the aggregate, more
than 9.9% of the outstanding Ordinary Shares (assuming conversion of all
convertible shares, including all 8% Preference Shares, then held by HM4 Triton
and its affiliates proposed to be sold) to any one buyer or related group of
buyers.
 
     Consent Rights of HM4 Triton. The Shareholders Agreement also provides that
so long as HM4 Triton and its affiliates continue to hold of record Ordinary
Shares and 8% Preference Shares (assuming conversion of such shares held by HM4
Triton and its affiliates into Ordinary Shares) after the Second Closing
representing in the aggregate at least (i) 50% of the Original Number or (ii)
10% of the outstanding Ordinary Shares (assuming the conversion or exchange of
all outstanding convertible or exchangeable securities of Triton), Triton may
not take certain actions without the consent of HM4 Triton, including the
following: (i) amend its Articles of Association or 8% Preference Shares
Authorization with respect to the voting powers, rights or preferences of the
holders of 8% Preference Shares, (ii) merge, consolidate or enter into a similar
business combination transaction or effect any reorganization, recapitalization
or other transaction pursuant to which a majority of the outstanding Ordinary
Shares or any 8% Preference Shares are exchanged for securities, cash or other
property, (iii) authorize, create or modify the terms of any series of
securities ranking prior to or pari passu with the 8% Preference Shares and
certain series of securities ranking junior to the 8% Preference Shares, (iv)
sell, lease or otherwise dispose of assets comprising in excess of 50% of the
market value of Triton and its subsidiaries or dissolve, liquidate or terminate
Triton, (v) pay certain dividends other than regular dividends on Triton's 5%
Preference Shares, (vi) create, incur, assume, guarantee or otherwise become
liable for additional indebtedness, or issue any preferred stock, unless
Triton's leverage ratio is less than 2.5 to 1, subject to certain exceptions,
(vii) issue additional shares of 8% Preference Shares, other than pursuant to
the Rights Offering and the Stock Purchase Agreement and in payment of
accumulated dividends on the outstanding 8% Preference Shares, (viii) issue any
shares of a class ranking pari passu with or prior to the 8% Preference Shares,
(ix) commence any tender offer or exchange offer for all or any portion of the
Ordinary Shares or (x) decrease the number of shares designated as 8% Preference
Shares.
 
     Registration Rights. In the Shareholders Agreement, Triton has granted
registration rights with respect to the 8% Preference Shares and any Ordinary
Shares then owned by HM4 Triton and its designated transferees (together, the
"Registrable Shares").
 
                                      S-29
<PAGE>   36
 
     The Shareholders Agreement provides that, at any time beginning one year
after the First Closing, one or more holders of Registrable Shares may (subject
to customary "black-out" periods) require Triton to effect up to five
registrations under the Securities Act; provided that the Registrable Shares
proposed to be sold represent more than 20% of the then outstanding Registrable
Shares, subject to certain limitations.
 
     The Shareholders Agreement also provides certain "piggyback" registration
rights to the holders of Registrable Shares whenever Triton proposes to register
an offering of any of its capital stock under the Securities Act (including on
behalf of any shareholder of Triton other than a holder of Registrable Shares),
subject to certain exceptions. HM4 Triton may also require Triton to file an
amendment to Triton's "shelf" registration statement to permit offerings of
Registrable Shares, whether pursuant to the demand registration or piggyback
registration rights of a holder of Registrable Shares, to be made thereafter
through such shelf.
 
     In addition, the Shareholders Agreement contains customary provisions
regarding the payment of holders' expenses relating to offerings by Triton in
connection with the exercise of registration rights and regarding mutual
indemnification of Triton and the holders of Registrable Shares for certain
securities law violations.
 
                    DESCRIPTION OF THE 8% PREFERENCE SHARES
 
     The following statements with respect to the 8% Preference Shares are
subject to the detailed provisions of the Unanimous Written Consent of the Board
of Directors of Triton Energy Limited Authorizing a Series of Preference Shares
(the "8% Preference Shares Authorization"), which has been filed as an exhibit
to Triton's Quarterly Report on Form 10-Q for the quarter ended September 30,
1998. See "Available Information" and "Incorporation of Certain Documents by
Reference" in the Prospectus accompanying this Prospectus Supplement. These
statements do not purport to be complete and, while Triton believes the
descriptions of the material provisions of the 8% Preference Shares
Authorization contained herein are accurate statements with respect to such
material provisions, such statements are subject to the detailed provisions in
the 8% Preference Shares Authorization, to which reference is hereby made for a
full description of such provisions.
 
DIVIDENDS
 
     The registered holders of 8% Preference Shares are entitled to receive, if
authorized or declared by the Board out of funds of Triton legally available for
payment, distributions in the form of cash dividends on each share at an annual
rate equal to 8.0% of the Liquidation Preference per share of the 8% Preference
Shares (defined to be $70 per share), payable for each semi-annual dividend
period ending June 30 and December 31 of each year (each, a "Dividend Period"),
beginning with the initial Dividend Period ending June 30, 1999. For each
Dividend Period, Triton will pay dividends on a date fixed by the Board that is
not later than five days after the end of such Dividend Period (each such date,
a "Dividend Payment Date"), except that if any such date is not a Business Day,
such payment shall be made on the Business Day immediately following such date.
A "Business Day" is defined as any day other than a Saturday, Sunday or a day on
which state or federally chartered banking institutions in New York City or
Dallas are not
 
                                      S-30
<PAGE>   37
 
required to be open. Such dividends begin to accumulate and will be fully
cumulative on a daily basis from the date on which an 8% Preference Share is
issued, whether or not authorized or declared by the Board and whether or not
there are funds legally available for the payment of such dividends. Dividends
will be paid to holders of record of 8% Preference Shares, as they appear on the
register of members of Triton at the close of business on the record dates
(which may not be more than 15 days preceding any payment date) fixed by the
Board. The amount of the dividend payable for each Dividend Period is the annual
dividend divided by two. The amount of dividends payable for any period other
than a full semi-annual Dividend Period is computed on the basis of a 360-day
year of twelve 30-day months. Dividends will be cumulative from the date the 8%
Preference Shares are first issued. HM4 Triton will receive a dividend, on the
date that the 8% Preference Shares are issued pursuant to the Rights Offering,
equal to the amount of the accumulated dividend on 1,822,500 8% Preference
Shares through that date.
 
     At the option of Triton, dividends may be paid, instead of in cash, on
declaration by the Board, by the issuance of additional fully paid whole shares
of 8% Preference Shares (the "Additional Shares") to the extent authorized but
unissued shares are legally available therefor. If any dividend payable on any
Dividend Payment Date is not declared or authorized and paid in full in cash on
such Dividend Payment Date, the amount payable as dividends that is not paid in
cash will be paid in Additional Shares, to the extent authorized but unissued
shares of 8% Preference Shares are legally available therefor. If a dividend is
to be paid in Additional Shares, the number of Additional Shares to be issued in
payment of the dividend with respect to each outstanding 8% Preference Share
will be determined by dividing (a) the amount of the accumulated dividend
payable to each registered holder of 8% Preference Shares on the basis of all
shares held of record by such holder as of the record date for such dividend by
(b) $70, with amounts in respect of any partial shares to be paid in cash by
Triton.
 
     Dividends on the 8% Preference Shares that are in arrears and unpaid (in
cash or Additional Shares) will cumulate as if such dividends had been paid in
Additional Shares and such Additional Shares were outstanding on each succeeding
dividend payment date until such accumulated semi-annual dividends have been
declared and paid in cash or Additional Shares. In the event dividends are in
arrears and unpaid for three or more Dividend Periods (whether or not
consecutive), holders of 8% Preference Shares will be entitled to certain voting
rights. See "-- Voting." Accumulated and unpaid dividends may be authorized or
declared and paid at any time, without reference to any regular Dividend Payment
Date, to holders of record on a record date fixed by the Board.
 
     So long as the 8% Preference Shares are outstanding, no full dividends will
be paid or set aside for payment on any class or series of Triton's capital
stock ranking on a parity as to dividends with the 8% Preference Shares ("Parity
Dividend Shares") unless full cumulative dividends on all outstanding 8%
Preference Shares for all dividend periods terminating on or prior to the
dividend payment date for such Parity Dividend Shares have been, or
contemporaneously are, paid or declared and set aside for payment. If full
dividends are not paid on the 8% Preference Shares, all dividends declared on
the 8% Preference Shares and any other Parity Dividend Shares will be declared
pro rata so that the ratio of the amount of dividends declared per share of the
8% Preference Shares to the dividends declared per share of the Parity Dividend
Shares is the same as the ratio of the accumulated and unpaid dividends per
share of the 8% Preference Shares to the
 
                                      S-31
<PAGE>   38
 
accumulated and unpaid dividends per share of the Parity Dividend Shares. In
addition, so long as the 8% Preference Shares are outstanding, no dividends may
be paid or set aside for payment on any class or series of Triton's capital
stock ranking junior as to dividends to the 8% Preference Shares ("Junior
Dividend Shares") unless full cumulative dividends on all outstanding 8%
Preference Shares for all dividend periods terminating on or prior to the
dividend payment date for such Junior Dividend Shares have been, or
contemporaneously are, paid or declared and set aside for payment. The 8%
Preference Shares will be junior as to dividends to any series or class of
Triton's shares hereafter issued which ranks senior as to dividends to the 8%
Preference Shares ("Senior Dividend Shares"), and if at any time Triton has
failed to pay or declare and set apart for payment accrued and unpaid dividends
on any Senior Dividend Shares, Triton may not pay any dividend on the 8%
Preference Shares.
 
     So long as the 8% Preference Shares are outstanding, Triton may not (i)
make any payment on account of the redemption, purchase, retirement or other
acquisition of any Parity Dividend Shares or any other class or series of
Triton's capital stock ranking on a parity with the 8% Preference Shares as to
distributions of assets upon voluntary or involuntary liquidation, dissolution
or winding up of Triton (any class or series ranking on a parity with the 8%
Preference Shares as to distributions of assets, "Parity Liquidation Shares") or
(ii) declare, pay or set aside for payment any distributions on Parity Dividend
Shares or Parity Liquidation Shares, other than certain dividends on Parity
Dividend Shares as described above, unless full cumulative dividends on all
outstanding 8% Preference Shares for all dividend periods ending on or before
such payment for, or setting aside for payment on account of, or the payment
date of such distributions on, such Parity Dividend Shares or Parity Liquidation
Shares have been or contemporaneously are paid or declared and set aside for
payment.
 
     So long as the 8% Preference Shares are outstanding, Triton may not make
any payment on account of the redemption, purchase, retirement or other
acquisition of any Junior Dividend Shares or any other class or series of
Triton's capital stock ranking junior to the 8% Preference Shares as to
distributions of assets upon voluntary or involuntary liquidation, dissolution
or winding up of Triton (any class or series ranking junior to the 8% Preference
Shares as to distributions of assets, "Junior Liquidation Shares") unless (i)
full cumulative dividends on all outstanding 8% Preference Shares and any other
Parity Dividend Shares have been, or contemporaneously are, paid or declared and
set aside for payment for all dividend periods with respect to the 8% Preference
Shares and any other Parity Dividend Shares terminating on or before such
payment for, or the setting aside for payment on account of, such class or
series of Junior Liquidation Shares and (ii) cash or Additional Shares
sufficient for the payment of the dividend for the current dividend period for
the 8% Preference Shares and any other Parity Dividend Shares have been paid or
set aside for payment. However, the foregoing restrictions do not apply to the
purchase or acquisition by Triton of Junior Liquidation Shares either (A)
pursuant to any employee or director incentive or benefit plan or arrangement or
(B) in exchange solely for Junior Shares (as defined herein).
 
LIQUIDATION PREFERENCE
 
     In the event of any voluntary or involuntary liquidation, dissolution or
winding up of Triton, before any payment or distribution of the assets of Triton
is made to or set aside
 
                                      S-32
<PAGE>   39
 
for the holders of Ordinary Shares, 5% Preference Shares and any other class or
series of Triton's capital stock ranking junior to the 8% Preference Shares as
to both dividends and liquidation rights (collectively, "Junior Shares"), the
holders of the 8% Preference Shares will be entitled to be paid, out of the
assets of Triton available for distribution to its shareholders, in immediately
available funds, $70 for each outstanding 8% Preference Share (including
outstanding Additional Shares) (the "Liquidation Preference"), plus an amount
equal to all dividends (whether or not authorized) accumulated and unpaid
thereon to the date of final distribution to such holders, but the holders of 8%
Preference Shares will not be entitled to receive the Liquidation Preference of
such shares until the liquidation preference of any other series or class of
Triton's shares hereafter issued which ranks senior as to liquidation rights to
the 8% Preference Shares ("Senior Liquidation Shares") has been paid in full.
Such holders of 8% Preference Shares will not be entitled to any further
payment. If, upon any liquidation, dissolution or winding up of Triton, the
assets of Triton, or proceeds thereof, distributable among the holders of the 8%
Preference Shares are insufficient to pay in full the Liquidation Preference
(plus accumulated and unpaid dividends, whether or not authorized, to the date
of final distribution to such holders) and liquidating payments on any other
shares of any class or series of Parity Liquidation Shares, then such assets, or
the proceeds thereof, will be distributed among the holders of 8% Preference
Shares and any such other Parity Liquidation Shares ratably in accordance with
the respective amounts that would be payable on such 8% Preference Shares and
any such other Parity Liquidation Shares if all amounts payable thereon were
paid in full.
 
CONVERSION
 
     The holders of the 8% Preference Shares are entitled to convert their 8%
Preference Shares into Ordinary Shares at any time, subject to the
qualifications described below, except that, with respect to 8% Preference
Shares called for redemption, conversion rights will expire at the close of
business on the fifth Business Day prior to the redemption date (unless Triton
defaults in the payment of the redemption price). No fractional shares will be
issued and, in lieu of any fractional share, Triton will pay a cash adjustment
based on the then current market price (determined as set forth in the 8%
Preference Shares Authorization) of the Ordinary Shares.
 
     Each 8% Preference Share is convertible initially into Ordinary Shares at
the rate of $17.50 per Ordinary Share (the "Conversion Price"), or four Ordinary
Shares. However, the Conversion Price is subject to adjustment as described
below.
 
     Holders of 8% Preference Shares at the close of business on a dividend
payment record date are entitled to receive the dividend payable on such shares
on the corresponding Dividend Payment Date, notwithstanding the conversion
thereof following such dividend payment record date on or prior to such Dividend
Payment Date.
 
     Upon the conversion of any 8% Preference Shares, the holder of each 8%
Preference Share converted is also entitled to receive an amount in cash equal
to all dividends (whether or not authorized or declared) accumulated and unpaid
on each 8% Preference Share converted, up to and including the effective date of
conversion. Such cash amount will be paid to the holder of the 8% Preference
Shares to which such dividends relate on or before the fifth Business Day after
the effective date of such conversion.
 
                                      S-33
<PAGE>   40
 
     The Conversion Price is subject to adjustment in certain circumstances,
including upon the issuance of Ordinary Shares at a price per share less than
the then current market price of Ordinary Shares, upon the issuance of Ordinary
Shares as a stock dividend, upon the combination or subdivision of Ordinary
Shares or issuance of capital stock upon reclassification of Ordinary Shares,
upon the issuance to Triton's shareholders of rights, options or warrants to
subscribe for or purchase Ordinary Shares at a price per share less than the
then current market price of Ordinary Shares and upon certain distributions to
Triton's shareholders of evidences of indebtedness, shares of Triton's capital
stock, cash or assets. No adjustment in the Conversion Price will be required
unless it would result in at least a one percent increase or decrease in the
Conversion Price; however, any adjustment not made will be carried forward.
 
     In case of any consolidation or merger of Triton with any other company, or
in the case of any merger of another company into Triton (other than a merger
with a company in which merger Triton is the continuing company and which does
not result in any reclassification, conversion, exchange or cancellation of
outstanding shares of Triton to another company), Triton will be required to
make proper provisions so that the holder of each 8% Preference Share then
outstanding (other than the person with which Triton consummated a merger or
consolidation or to whom such a sale or transfer was made) will have the right
thereafter to convert such 8% Preference Share into the kind or amount of shares
of stock and other securities and property receivable upon such consolidation,
merger, sale or conveyance by a holder of the number of Ordinary Shares into
which such 8% Preference Share might have been converted immediately prior to
such consolidation, merger, sale or conveyance.
 
     Triton must pay all issue or transfer taxes that may be imposed with
respect to the issue or delivery of Ordinary Shares upon conversion of 8%
Preference Shares but will not be required to pay any transfer taxes incurred as
a result of the issuance of Ordinary Shares in a name other than that of the
registered holder of the converted 8% Preference Shares.
 
                                      S-34
<PAGE>   41
 
REDEMPTION AT THE OPTION OF TRITON
 
     Triton may not redeem the 8% Preference Shares prior to September 30, 2001
(the "First Redemption Date"). On and after the First Redemption Date, Triton
will have the right and option (provided it has sufficient funds legally
available therefor), but not the obligation, to redeem all, but not less than
all, of the then outstanding 8% Preference Shares at any time that the average
of the current market price per share of the Ordinary Shares for the 20 trading
days immediately preceding the date on which notice of redemption is given (the
"Average Market Value") is equal to or greater than the Average Market Value per
Ordinary Share corresponding to the six-month period in which the notice date
falls, as set forth below:
 
<TABLE>
<CAPTION>
REDEMPTION NOTICE GIVEN ON SIX MONTHS ENDING          AVERAGE MARKET VALUE
<S>                                                   <C>
March 31, 2002.....................................          $28.54
September 30, 2002.................................          $31.14
March 31, 2003.....................................          $34.20
September 30, 2003.................................          $37.58
March 31, 2004.....................................          $32.57
September 30, 2004.................................          $34.97
March 31, 2005.....................................          $37.60
</TABLE>
 
     From and after April 1, 2005, the minimum Average Market Value per Ordinary
Share will be increased every six months to reflect an internal rate of return
of 20% for a holder purchasing 8% Preference Shares as of the date the first 8%
Preference Share was issued. The minimum Average Market Values set forth above
may be adjusted in the event of any combination, subdivision or reclassification
of Ordinary Shares, or any similar event.
 
     Any redemption of the 8% Preference Shares will be for an amount payable in
cash equal to $70 per share plus an amount payable in cash equal to all
accumulated and unpaid dividends on the 8% Preference Shares, whether or not
authorized or declared, to and including the date fixed for redemption. Triton
shall give written notice of redemption to each holder of record of 8%
Preference Shares, which shall specify a date fixed for redemption no less than
30 nor more than 60 days after the date of such notice.
 
VOTING
 
     Each 8% Preference Share will have one vote per share, except that when the
8% Preference Shares and the Ordinary Shares vote together as a single class,
then each holder of the 8% Preference Shares will be entitled to the number of
votes with respect to such holder's 8% Preference Shares equal to the number of
whole Ordinary Shares into which such 8% Preference Shares would have been
converted at the Conversion Price in effect on the record date for determining
shareholders entitled to vote on such matters.
 
     The holders of 8% Preference Shares will vote together as a single class
with the holders of the Ordinary Shares on an as converted basis on all matters
submitted to a vote of the holders of the Ordinary Shares. Under Triton's
Articles of Association, the rights attached to the 8% Preference Shares may be
varied only with the consent in writing of the holders of all outstanding 8%
Preference Shares, or by a vote of the holders of at least
 
                                      S-35
<PAGE>   42
 
two thirds of the 8% Preference Shares represented in person or by proxy at a
duly convened meeting, voting separately as a class. In addition, pursuant to
the 8% Preference Shares Authorization, a two-thirds vote of the outstanding 8%
Preference Shares will be required to create a class of equity securities senior
to the 8% Preference Shares (other than out of Triton's existing 20,000,000
authorized shares of "blank check" preferred stock, 11,000,000 of which
currently are designated as 8% Preference Shares and 420,000 of which currently
are designated as 5% Preference Shares) or to adopt charter amendments
materially adversely affecting the rights of the 8% Preference Shares. A
majority vote of the 8% Preference Shares will be required to increase the
authorized number of 8% Preference Shares or to create a class of equity
securities ranking pari passu with the 8% Preference Shares (in each case, other
than out of Triton's existing 20,000,000 authorized shares of "blank check"
preferred stock, 11,000,000 of which currently are designated as 8% Preference
Shares and 420,000 of which currently are designated as 5% Preference Shares).
Other than as described herein, the holders of 8% Preference Shares will have no
voting rights, except as required by the charter of Triton and applicable law.
 
     If and whenever three or more semi-annual dividends (whether or not
consecutive) payable on the 8% Preference Shares are in arrears, whether or not
authorized, the number of directors then constituting the Board of Directors
will be increased by two, and the holders of the 8% Preference Shares, voting
separately as a class, will be entitled to elect two additional directors to
serve on the Board at any annual meeting of shareholders or extraordinary
meeting held for the purpose of electing directors, or at an extraordinary
meeting of the holders of the 8% Preference Shares called for the purpose of
electing directors. At the next annual meeting of shareholders of Triton
following any such election and each succeeding annual meeting, for so long as
all arrears in dividends on the 8% Preference Shares then outstanding have not
been paid and the holders of 8% Preference Shares elect to exercise such right,
the holders of 8% Preference Shares, voting separately as a class, will have the
right to elect two directors to the Board. When all arrears in dividends on the
8% Preference Shares then outstanding have been paid, then the right of the
holders of the 8% Preference Shares to elect such additional directors will
cease (but subject always to the same provision for the vesting of such voting
rights in the case of any similar future arrearages in three or more semi-annual
dividends), the terms of office of all persons elected as directors to the two
directorships created as a result of the arrearage will terminate and the number
of members of the Board will be reduced accordingly.
 
TRANSFERABILITY
 
     The 8% Preference Shares offered hereby, and the Ordinary Shares issuable
upon conversion thereof, have been registered under the Securities Act and the
Exchange Act. Accordingly, the 8% Preference Shares and Ordinary Shares issuable
upon conversion thereof will generally be freely transferable by the holders
thereof.
 
     Triton has entered into a Shareholders Agreement with HM4 Triton providing
for certain registration rights. See "Investment by Hicks Muse -- Shareholders
Agreement."
 
     The 8% Preference Shares have been approved for listing on the New York
Stock Exchange under the symbol "OILPrA," subject to satisfaction of the New
York Stock Exchange's minimum distribution requirements and subject to official
notice of issuance. See "Risk Factors -- Market Considerations -- 8% Convertible
Preference Shares."
 
                                      S-36
<PAGE>   43
 
                 CERTAIN U.S. FEDERAL INCOME TAX CONSIDERATIONS
 
GENERAL
 
     The following is a general discussion of certain United States federal
income tax consequences of the Rights Offering to United States persons (as
defined below) that currently own Ordinary Shares and 5% Preference Shares. This
discussion is based on the provisions of the Internal Revenue Code of 1986, as
amended (the "Code"), and regulations, rulings and judicial decisions thereunder
as of the date hereof, and such authorities may be repealed, revoked or modified
so as to result in federal income tax consequences different from those
discussed below. This discussion does not purport to deal with all aspects of
federal income taxation that may be relevant to a particular holder of Rights or
8% Preference Shares acquired upon the exercise of Rights (the "Right Preference
Shares") in light of such holder's personal investment circumstances, nor does
this discussion address special tax implications which may be applicable to
certain types of holders of Rights or Right Preference Shares subject to special
treatment under the Code (including, without limitation, financial institutions,
broker-dealers, regulated investment companies, life insurance companies,
tax-exempt organizations, foreign corporations and non-resident aliens).
Moreover, the discussion is limited to persons who will hold the Rights and any
Right Preference Shares as capital assets within the meaning of Section 1221 of
the Code. No consideration of any aspects of state, local or foreign taxation is
included herein. Triton has not sought, nor does it intend to seek, any rulings
from the Internal Revenue Service relating to the tax issues addressed herein,
and such issues may be subject to substantial uncertainty resulting from the
lack of definitive judicial or administrative authority and interpretations
applicable thereto.
 
     As used herein, a United States person means a person that is (i) a citizen
or resident of the United States, (ii) a corporation or partnership created or
organized in or under the laws of the United States or any political subdivision
thereof, (iii) an estate the income of which is subject to United States federal
income taxation regardless of its source or (iv) a trust which is subject to the
supervision of a court within the United States and the control of one or more
United States persons as described in Section 7701(a)(30) of the Code.
 
     EACH HOLDER IS URGED TO CONSULT HIS OWN TAX ADVISOR AS TO THE SPECIFIC TAX
CONSEQUENCES OF THE RIGHTS OFFERING WITH RESPECT TO HIS OWN PARTICULAR TAX
SITUATION, INCLUDING THE APPLICATION AND EFFECT OF THE CODE, AS WELL AS STATE,
LOCAL AND FOREIGN INCOME AND OTHER TAX LAWS.
 
TAX CONSEQUENCES OF RIGHTS OFFERING TO HOLDERS OF ORDINARY SHARES
 
     Issuance of Rights. Current law is not clear as to whether the distribution
of Rights to holders of Ordinary Shares (the "Ordinary Shareholders") would be
characterized as a distribution under Section 305(a) of the Code (a "Section
305(a) Distribution") or, alternatively, as a distribution under Sections 301
and 305(b) of the Code (a "Section 301 Distribution"). Triton intends to take
the position that the Rights distribution is properly characterized as a Section
305(a) Distribution. Assuming that the Rights distribution is properly
characterized as a Section 305(a) Distribution, the distribution would be
 
                                      S-37
<PAGE>   44
 
nontaxable without regard to Triton's current and accumulated earnings and
profits. If the Rights distribution were treated as a Section 301 Distribution,
the value of the Rights, if any, would be treated as a taxable dividend to the
Ordinary Shareholders to the extent paid from Triton's current or accumulated
earnings and profits, as determined under United States federal income tax
principles. Such dividends would not be eligible for the dividends received
deduction allowed to corporations under the Code. Any amount in excess of
Triton's current and accumulated earnings and profits would be treated as a
nontaxable reduction in the Ordinary Shareholder's basis in his Ordinary Shares,
and the balance, if any, in excess of such adjusted basis would be taxed as
capital gain.
 
     Basis of Rights. If the Rights distribution is properly characterized as a
Section 305(a) Distribution, then, except as provided in the following sentence,
the tax basis of Rights received by an Ordinary Shareholder in the Rights
distribution would be zero. If, however, the Rights distribution constitutes a
Section 305(a) Distribution and either (i) the Rights have a value (on the date
of distribution of the Rights) equal to or greater than 15% of the value of the
Ordinary Shares with respect to which the Rights are distributed or (ii) the
Ordinary Shareholder elects to apply the rule described in this sentence, then
upon exercise or transfer (but not upon lapse) of the Rights, the Ordinary
Shareholder would reallocate his tax basis in his Ordinary Shares between the
Rights and the Ordinary Shares based on the relative fair market values of each.
 
     If the Rights distribution is properly characterized as a Section 301
Distribution, an Ordinary Shareholder will have a tax basis in the Rights equal
to the fair market value of the Rights on the date of the Rights distribution.
 
     Holding Period of Rights. If the Rights distribution is properly
characterized as a Section 305(a) Distribution, an Ordinary Shareholder will
have a holding period in the Rights that includes the holding period of the
Ordinary Shares to which the Rights distribution relates.
 
     If the Rights distribution were treated as a Section 301 Distribution, the
Ordinary Shareholder would have a holding period in the Rights that begins on
the day following the date of distribution of the Rights.
 
     Exercise or Sale of Rights. A holder of Rights will not be taxed upon
exercise of the Rights. The holder's tax basis in the shares of Right Preference
Shares received upon exercise will equal (i) his basis in the Rights, plus (ii)
the exercise price paid for the Right Preference Shares. The holder's holding
period in the Right Preference Shares will begin on the day following the date
of exercise of the Rights.
 
     If the Rights distribution is properly characterized as a Section 305(a)
Distribution, then under Section 306 of the Code, subject to certain exceptions,
a holder of Rights will realize ordinary income upon the sale of Rights in an
amount equal to the amount, if any, that would have been treated as a dividend
if the distribution of the Rights had constituted a Section 301 Distribution,
but not in excess of the amount realized upon the sale. If the amount realized
upon the sale exceeds the sum of the amount included as ordinary income and the
holder's tax basis in the Rights, such excess will be treated as capital gain.
No capital loss will be recognized. If the amount realized is less than the sum
of the amount included as ordinary income and the holder's tax basis in the
Rights, the difference will increase the holder's tax basis in its Ordinary
Shares. Notwithstanding the above, if (i) the transferee is not a person whose
ownership of stock would be attributable to such holder
 
                                      S-38
<PAGE>   45
 
under Section 318(a) of the Code and (ii) the disposition of the Rights
terminates the entire stock interest of the holder in Triton after giving effect
to the constructive ownership rules of Section 318(a) of the Code, the holder
will generally recognize capital gain or loss on the sale of Rights in an amount
equal to the difference between the amount realized on the sale and the holder's
tax basis in the Rights sold, with no portion being treated as ordinary income.
Other exceptions to the application of Section 306 include (i) if, with respect
to the Rights distribution, Triton has no current and accumulated earnings and
profits and (ii) if it is established to the satisfaction of the Secretary of
the Treasury that the Rights distribution and the disposition were not in
pursuance of a tax avoidance plan (the "Additional 306 Exceptions").
 
     Lapse of Rights. If the Rights distribution is properly characterized as a
Section 301 Distribution, a holder of Rights who allows the Rights to lapse
would have a capital loss equal to his basis, if any, in the Rights that lapsed.
If the Rights distribution is properly characterized as a Section 305(a)
Distribution, an Ordinary Shareholder who allows a Right to lapse will have no
basis in the Right and, thus, would realize no capital loss.
 
     Constructive Dividend. The Conversion Price of the Right Preference Shares
which would be acquired upon exercise of the Rights is subject to adjustment in
certain circumstances. Under Section 305(c) of the Code, adjustments that would
have the effect of increasing the proportionate interest of holders of the Right
Preference Shares in the assets or earnings of Triton will in some circumstances
give rise to a deemed distribution to holders of the Rights. Such deemed
distribution would be taxable as ordinary income to the extent of Triton's
current and accumulated earnings and profits and would not be eligible for the
dividends received deduction allowed to corporations under the Code.
 
     Information Reporting and Backup Withholding. In general, information
reporting requirements will apply to the proceeds received on the sale of the
Rights paid within the United States (and in certain cases, outside the United
States) to holders other than certain exempt recipients (such as corporations),
and a 31 percent backup withholding may apply to such amounts if the holder
fails to provide an accurate taxpayer identification number or to report
interest and dividends required to be shown on its federal income tax returns.
The amount of any backup withholding from a payment to a holder will be allowed
as a credit against the holder's United States federal income tax liability.
 
TAX CONSEQUENCES OF RIGHTS OFFERING TO HOLDERS OF 5% PREFERENCE SHARES
 
     Issuance of Rights. The distribution of Rights to holders of 5% Preference
Shares (the "Preference Shares" and "Preference Shareholders") will be
characterized as a Section 301 Distribution. Therefore, the value of the Rights,
if any, will be treated as a taxable dividend to the Preference Shareholders to
the extent paid from Triton's current or accumulated earnings and profits. Such
dividends will not be eligible for the dividends received deduction allowed to
corporations under the Code. Any amount in excess of Triton's current and
accumulated earnings and profits will be treated as a nontaxable reduction in
the tax basis of the Preference Shares, and the balance, if any, in excess of
such tax basis will be taxed as capital gain.
 
     Basis of Rights. A Preference Shareholder will have a tax basis in the
Rights equal to the fair market value of the Rights, if any, on the date of the
Rights distribution.
 
                                      S-39
<PAGE>   46
 
     Holding Period of Rights. A Preference Shareholder will have a holding
period in the Rights that begins on the day following the date of distribution
of the Rights.
 
     Exercise or Sale of Rights. A holder of Rights received in respect of
Preference Shares will not be taxed upon exercise of the Rights. The holder's
tax basis in the Right Preference Shares received upon exercise will equal (i)
the holder's basis in the Rights, plus (ii) the exercise price paid for the
Right Preference Shares. The holder's holding period in the Right Preference
Shares will begin on the day following the date of exercise of the Rights. Upon
a sale of the Rights, a holder of Rights will generally realize capital gain or
loss equal to the difference between the amount received, if any, for the Rights
and the holder's tax basis in the Rights.
 
     Lapse of Rights. A holder of Rights received in respect of Preference
Shares who allows Rights to lapse would have a capital loss equal to his basis
in the Rights that lapsed.
 
     Information Reporting and Backup Withholding. In general, information
reporting requirements will apply to the distribution of Rights and the proceeds
received on the sale of the Rights paid within the United States (and in certain
cases, outside the United States) to holders other than certain exempt
recipients (such as corporations), and a 31 percent backup withholding may apply
to such amounts if the holder fails to provide an accurate taxpayer
identification number or to report interest and dividends required to be shown
on its federal income tax returns. The amount of any backup withholding from a
payment to a holder will be allowed as a credit against the holder's United
States federal income tax liability.
 
TAX CONSEQUENCES OF OWNERSHIP OF RIGHT PREFERENCE SHARES
 
     Dividends on Right Preference Shares. The amount of cash and the fair
market value of any 8% Preference Shares received by a holder as a distribution
on Right Preference Shares will be treated as ordinary dividend income to the
extent of Triton's current and accumulated earnings and profits that are
allocable to such Right Preference Shares. Such dividends will not be eligible
for the dividends received deduction allowed to corporations under the Code. The
amount of the distribution in excess of Triton's current and accumulated
earnings and profits will reduce the holder's tax basis in his Right Preference
Shares until such basis is reduced to zero, and any excess will be treated as
capital gain.
 
     Sale of Right Preference Shares. The consequences of a sale of Right
Preference Shares will depend, in part, upon whether the holder of the Right
Preference Shares was an Ordinary Shareholder or Preference Shareholder at the
time the Rights were distributed (an "Original Ordinary Shareholder" or
"Original Preference Shareholder," respectively) and whether the Rights
distribution is properly characterized as a Section 305(a) Distribution. If the
Rights distribution is properly characterized as a Section 305(a) Distribution,
then under Section 306 of the Code, subject to certain exceptions, an Original
Ordinary Shareholder will realize ordinary income on a sale of the Right
Preference Shares in an amount equal to the amount, if any, that would have been
treated as a dividend if the distribution of the Rights had constituted a
Section 301 Distribution, but not in excess of the amount realized upon the
sale. If the amount realized upon the sale exceeds the sum of the amount
included as ordinary income and the holder's tax basis in the Right Preference
Shares, such excess will be treated as capital gain. No capital loss will be
 
                                      S-40
<PAGE>   47
 
recognized. If the amount realized is less than the sum of the amount included
as ordinary income and the holder's tax basis in the Right Preference Shares,
the difference will increase the holder's tax basis in any Ordinary Shares.
Notwithstanding the above, if (i) the transferee is not a person whose ownership
of stock would be attributable to such holder under Section 318(a) of the Code
and (ii) the disposition of the Right Preference Shares terminates the entire
stock interest of the holder in Triton after giving effect to the constructive
ownership rules of Section 318(a) of the Code, or if one of the Additional 306
Exceptions applies, the holder will generally recognize capital gain or loss in
an amount equal to the difference between the amount realized on the sale and
the holder's tax basis in the Right Preference Shares sold, with no portion
being treated as ordinary income.
 
     An Original Preference Shareholder (and an Original Ordinary Shareholder if
the Rights distribution were properly characterized as a Section 301
Distribution or otherwise not subject to Section 306) will generally recognize
capital gain or loss in an amount equal to the difference between the amount
realized on the sale and the holder's tax basis in the Right Preference Shares
sold.
 
     Cash Redemption of Right Preference Shares. The consequences of a
redemption of Right Preference Shares will depend, in part, upon whether the
holder is an Original Ordinary Shareholder subject to Section 306 or to Section
301 or an Original Preference Shareholder. If the Rights distribution is
properly characterized as a Section 305(a) Distribution, then under Section 306
of the Code, subject to certain exceptions, cash proceeds received upon a
redemption by an Original Ordinary Shareholder will generally be treated as a
taxable dividend to the extent of such holder's proportionate share of Triton's
current and accumulated earnings and profits. Such dividends will not be
eligible for the dividends received deduction allowed to corporations under the
Code. The amount of redemption proceeds, if any, in excess of Triton's current
and accumulated earnings and profits would be treated as a nontaxable reduction
in the Ordinary Shareholder's tax basis in his Right Preference Shares redeemed,
and the balance, if any, in excess of such adjusted basis would be taxed as
capital gain. No capital loss will be recognized. Any remaining basis in the
Right Preference Shares in excess of the redemption proceeds should increase the
holder's tax basis in any Ordinary Shares. Notwithstanding the above, if the
redemption of the Right Preference Shares terminates the entire stock interest
of the Original Ordinary Shareholder in Triton after giving effect to the
constructive ownership rules of Section 318(a) of the Code, or if one of the
Additional 306 Exceptions applies, and the redemption would otherwise qualify as
a sale or exchange under the Section 302 tests described below, the holder will
generally recognize capital gain or loss in an amount equal to the difference
between the amount received upon the redemption and the holder's tax basis in
the Right Preference Shares sold.
 
     The redemption of Right Preference Shares held by an Original Preference
Shareholder (or by an Original Ordinary Shareholder if the Rights distribution
were properly characterized as a Section 301 Distribution or otherwise not
subject to Section 306) will be treated, under Section 302 of the Code, either
as a dividend or as a sale or exchange giving rise to capital gain or loss. If a
redemption of Right Preference Shares is treated as a dividend with respect to a
particular Original Preference Shareholder under Section 302 of the Code, such
holder will recognize dividend income (rather than capital gain) in an amount
equal to the cash received without regard to the holder's basis
 
                                      S-41
<PAGE>   48
 
in the Right Preference Shares, to the extent of its proportionate share of
Triton's current and accumulated earnings and profits. Pursuant to Section 302
of the Code, the redemption will not be treated as a dividend, if after giving
effect to the constructive ownership rules of Section 318 of the Code, the
redemption (i) represents a "complete termination" of the holder's stock
interest in Triton, (ii) is "substantially disproportionate" with respect to the
exchanging holder or (iii) is "not essentially equivalent to a dividend" with
respect to the exchanging holder, all within the meaning of Section 302(b) of
the Code. An exchange will be "not essentially equivalent to a dividend" as to a
particular holder if it results in a "meaningful reduction" in such holder's
interest in Triton (after application of the constructive ownership rules of
Section 318 of the Code). In general, there are no fixed rules for determining
whether a "meaningful reduction" has occurred. EACH HOLDER SHOULD CONSULT ITS
OWN TAX ADVISOR AS TO ITS ABILITY IN LIGHT OF ITS OWN PARTICULAR CIRCUMSTANCES
TO SATISFY ANY OF THE FOREGOING TESTS.
 
     Receipt of Ordinary Shares Upon Conversion of Right Preference
Shares. Except to the extent of any dividends paid upon conversion, the
conversion of shares of Right Preference Shares into Ordinary Shares will be
nontaxable to the holders of Rights. Each holder's basis and holding period in
the Ordinary Shares received will be the same as his basis and holding period in
the shares of Right Preference Shares surrendered therefor. Gain or loss
recognized on a sale of Ordinary Shares will generally be capital gain or loss.
 
     Constructive Dividend. The Conversion Price of the Right Preference Shares
is subject to adjustment in certain circumstances. Under Section 305(c) of the
Code, adjustments that would have the effect of increasing the proportionate
interest of holders of the Right Preference Shares in the assets or earnings of
Triton will in some circumstances give rise to a deemed distribution to such
holders. The deemed distribution would be taxable as ordinary income to the
extent of Triton's current and accumulated earnings and profits and would not be
eligible for the dividends received deduction allowed to corporations under the
Code.
 
INFORMATION REPORTING AND BACKUP WITHHOLDING
 
     In general, information reporting requirements will apply to dividends paid
in respect of the Right Preference Shares and the proceeds received on the sale,
exchange or redemption of the Right Preference Shares paid within the United
States (and in certain cases, outside of the United States) to holders other
than certain exempt recipients (such as corporations), and a 31 percent backup
withholding may apply to such amounts if the holder fails to provide an accurate
taxpayer identification number or to report interest and dividends required to
be shown on its federal income tax returns. The amount of any backup withholding
from a payment to a holder will be allowed as a credit against the holder's
United States federal income tax liability.
 
                                      S-42
<PAGE>   49
 
                                  Triton Logo
 
                              SUBSCRIPTION AGENT:
 
                    ChaseMellon Shareholder Services, L.L.C.
 
                                    By Mail:
 
                    ChaseMellon Shareholder Services, L.L.C.
                              Post Office Box 3301
                           South Hackensack, NJ 07606
                        Attn: Reorganization Department
 
                                    By Hand:
 
                    ChaseMellon Shareholder Services, L.L.C.
                            120 Broadway, 13th Floor
                               New York, NY 10271
                        Attn: Reorganization Department
 
                             By Overnight Delivery:
 
                    ChaseMellon Shareholder Services, L.L.C.
                     85 Challenger Road -- Mail Drop Reorg.
                           Ridgefield Park, NJ 07660
                        Attn: Reorganization Department
 
                     Telephone (toll-free): (877) 698-6867
                           Facsimile: (201) 296-4293
                 Facsimile confirmation number: (201) 296-4860
                            ------------------------
 
                               INFORMATION AGENT:
 
                    ChaseMellon Shareholder Services, L.L.C.
                        450 West 33rd Street, 14th Floor
                               New York, NY 10001
 
                 Banks and brokers call collect: (212) 273-8070
                   All others call toll-free: (877) 698-6867
                            ------------------------
 
                                DEALER MANAGER:
 
              Donaldson, Lufkin & Jenrette Securities Corporation
                                277 Park Avenue
                               New York, NY 10172
                      Telephone (collect): (212) 892-7737


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