<PAGE>   1

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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------

                                   FORM 10-Q

<TABLE>
<S>       <C>                                                          <C>
[X]             QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
               FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1999
                                       OR
[ ]            TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
</TABLE>

             FOR THE TRANSITION PERIOD FROM ________ TO ________ .
                         COMMISSION FILE NUMBER 0-8565

                             MARINE PETROLEUM TRUST
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                            <C>
                    TEXAS                                        75-6008017
         (State or other jurisdiction                         (I.R.S. Employer
      of incorporation or organization)                     Identification No.)
            BANK OF AMERICA, N.A.                                75283-0241
        P.O. BOX 830241, DALLAS, TEXAS                           (Zip Code)
   (Address of principal executive offices)
</TABLE>

       Registrant's telephone number, including area code (800) 985-0794

                                      None
              (Former name, former address and former fiscal year
                         if changed since last report)
                             ---------------------

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

                             Yes   X       No _____

     Indicate number of units of beneficial interest outstanding as of the last
practicable date.

<TABLE>
<CAPTION>
         Title of Each Class of Units              Number of Units of Beneficial Interest
            of Beneficial Interest                           September 30, 1999
         ----------------------------              --------------------------------------
<S>                                            <C>
         UNITS OF BENEFICIAL INTEREST                            2,000,000
</TABLE>

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<PAGE>   2

                             MARINE PETROLEUM TRUST

                                     INDEX

<TABLE>
<CAPTION>
                                                               PAGE
                                                              NUMBER
                                                              ------
<S>                                                           <C>
PART I. FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS (UNAUDITED)....................     2

Condensed Consolidated Balance Sheets September 30, 1999 and
  June 30, 1999.............................................     2

Condensed Consolidated Statements of Income and
  Undistributed Income for the Three Months Ended September
  30, 1999 and 1998.........................................     3

Condensed Consolidated Statements of Cash Flows for the
  Three Months Ended September 30, 1999 and 1998............     4

Notes to Condensed Consolidated Financial Statements........     5

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
CONDITION AND RESULTS OF
        OPERATIONS..........................................     6

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT
  MARKET RISK...............................................     7

PART II. OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K....................     8

Signatures..................................................     9

Exhibit Index...............................................    10
</TABLE>
<PAGE>   3

                         PART I. FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

                     CONDENSED CONSOLIDATED BALANCE SHEETS
                      SEPTEMBER 30, 1999 AND JUNE 30, 1999
                                  (UNAUDITED)

                                     ASSETS

<TABLE>
<CAPTION>
                                                              SEPTEMBER 30     JUNE 30
                                                                  1999           1999
                                                              ------------    ----------
<S>                                                           <C>             <C>
Current Assets:
  Cash and cash equivalents.................................   $1,609,565     $1,659,864
  Oil and gas royalties receivable..........................      426,879        307,657
  Receivable from affiliate.................................      119,411         80,939
                                                               ----------     ----------
          Total current assets..............................    2,155,855      2,048,460
                                                               ----------     ----------
Investment in affiliate.....................................      298,636        322,070
Office equipment, net.......................................          555            555
Producing oil and gas properties............................            7              7
                                                               ----------     ----------
                                                               $2,455,053     $2,371,092
                                                               ==========     ==========

                              LIABILITIES AND TRUST EQUITY

Current Liabilities:
  Accounts payable..........................................   $  122,923     $  244,250
  Income taxes payable......................................       10,696         10,156
                                                               ----------     ----------
          Total current liabilities.........................      133,619        254,406
                                                               ----------     ----------
Trust Equity:
  Corpus -- authorized 2,000,000 units of beneficial
     interest, issued 2,000,000 units at nominal value......            8              8
  Undistributed income......................................    2,321,426      2,116,678
                                                               ----------     ----------
          Total trust equity................................    2,321,434      2,116,686
                                                               ----------     ----------
                                                               $2,455,053     $2,371,092
                                                               ==========     ==========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.

                                        2
<PAGE>   4

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

      CONDENSED CONSOLIDATED STATEMENTS OF INCOME AND UNDISTRIBUTED INCOME
             FOR THE THREE MONTHS ENDED SEPTEMBER 30, 1999 AND 1998
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                                   THREE MONTHS
                                                              -----------------------
                                                                 1999         1998
                                                              ----------   ----------
<S>                                                           <C>          <C>
Income:
  Oil and gas royalties.....................................  $1,004,437   $  669,234
  Equity in earnings of affiliate...........................      86,481       48,442
  Interest income...........................................      22,318       26,486
                                                              ----------   ----------
                                                               1,113,236      744,162
Expenses -- General and administrative......................      33,834       58,382
                                                              ----------   ----------
          Income before Federal income taxes................   1,079,402      685,780
Federal income taxes of subsidiary..........................       2,140           --
                                                              ----------   ----------
          Net income........................................   1,077,262      685,780
Undistributed income at beginning of period.................   2,116,678    1,809,260
                                                              ----------   ----------
                                                               3,193,940    2,495,040
Distributions to unitholders................................     872,514      651,339
                                                              ----------   ----------
Undistributed income at end of period.......................  $2,321,426   $1,843,701
                                                              ==========   ==========
Net income per unit.........................................  $     0.54   $     0.34
                                                              ==========   ==========
Distributions per unit......................................  $     0.44   $     0.33
                                                              ==========   ==========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.

                                        3
<PAGE>   5

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

                CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
             FOR THE THREE MONTHS ENDED SEPTEMBER 30, 1999 AND 1998
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                                 1999          1998
                                                              ----------    ----------
<S>                                                           <C>           <C>
Cash flows from operating activities:
  Net income................................................  $1,077,262    $  685,780
  Adjustments to reconcile net income to net cash provided
     by operating activities:
     Equity in undistributed earnings of affiliate..........      23,434        81,724
     Change in assets and liabilities:
       Oil and gas royalties receivable.....................    (119,222)      106,976
       Receivable from affiliate............................     (38,472)      (19,508)
       Accounts payable.....................................    (121,327)     (297,650)
       Income taxes payable.................................         540        (2,200)
                                                              ----------    ----------
          Net cash provided by operating activities.........     822,215       555,122
                                                              ----------    ----------
Cash flows from financing activities -- distributions to
  unitholders...............................................    (872,514)     (651,339)
                                                              ----------    ----------
          Net decrease in cash and cash equivalents.........     (50,299)      (96,217)
                                                              ----------    ----------
Cash and cash equivalents at beginning of period............   1,659,864     1,922,336
                                                              ----------    ----------
Cash and cash equivalents at end of period..................  $1,609,565    $1,826,119
                                                              ==========    ==========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.

                                        4
<PAGE>   6

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                               SEPTEMBER 30, 1999
                                  (UNAUDITED)

ACCOUNTING POLICIES

     The financial statements include the financial statements of Marine
Petroleum Trust (the "Trust") and its wholly-owned subsidiary, are condensed,
and should be read in conjunction with the Trust's annual report on Form 10-K
for the fiscal year ended June 30, 1999. The financial statements included
herein are unaudited, but in the opinion of management include all adjustments
necessary for a fair presentation of the results of operations for the periods
indicated. Operating results for the three months ended September 30, 1999 are
not necessarily indicative of the results that may be expected for the year
ending June 30, 2000.

UNDISTRIBUTED INCOME

     Undistributed income on September 30, 1999 includes $1,521,489 applicable
to the Trust and $799,937 applicable to Marine Petroleum Corporation, the
Trust's wholly-owned subsidiary. Distributions to unitholders are dependent on
the volume and price of oil and gas sold by others and will fluctuate from
quarter to quarter.

ACCOUNTS PAYABLE

     Marine Petroleum Corporation has provided an account payable of $120,250 to
cover possible refunds that may be required upon redetermination of gas prices
for royalty payments in prior periods. During the current quarter, Marine
Petroleum Corporation determined that $124,000 of the previously established
account payable was no longer required. Accordingly accounts payable was reduced
and oil and gas royalties was increased by $124,000.

                                        5
<PAGE>   7

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS

FINANCIAL CONDITION -- LIQUIDITY AND CAPITAL RESOURCES

     The Trust is a "royalty trust" with overriding royalty interests in oil and
gas leases in the Gulf of Mexico. The Trust's indenture (and the charter and
by-laws of its subsidiary) expressly prohibit the operation of any kind of trade
or business. All royalties received by the Trust, less administrative expenses,
are distributed quarterly to unitholders. Since the Trust's sole purpose is to
collect and distribute cash collected from royalties, there are no requirements
for capital.

GENERAL

     The Trust's net income for the current quarter was up 57% over that of the
comparable quarter last year and reflects the increase realized in the average
prices of both oil and gas. Oil production was up 82% over the comparable
quarter a year ago and the average price realized was up 34%. Gas production was
down 5% but was offset by a 25% increase in its average price.

     Operators of the leases in which the Trust has an interest drilled or
recompleted 2 oil wells and 7 gas wells during the current quarter.

     The following table presents the net production quantities of oil and gas
and net income and distributions per unit for the last five quarters.

<TABLE>
<CAPTION>
                                                                PRODUCTION
                                                          ----------------------    NET         CASH
QUARTER                                                   OIL(BBLS)    GAS(MCF)    INCOME   DISTRIBUTION
-------                                                   ----------   ---------   ------   ------------
<S>                                                       <C>          <C>         <C>      <C>
September 30, 1998......................................    12,844      223,920     $.34        $.33
December 31, 1998.......................................    16,382      346,495      .46         .41
March 31, 1999..........................................    17,496      279,145      .37         .31
June 30, 1999...........................................    15,017      147,655      .36         .35
September 30, 1999......................................    23,388      213,537      .54         .44
</TABLE>

     The Trust's revenues are derived from the oil and gas production activities
of unrelated parties. The Trust's revenues and distributions fluctuate from
period to period based upon factors beyond the Trust's control, including
without limitation the number of productive wells drilled and maintained on
leases subject to the Trust's interest, the level of production over time from
such wells and the prices at which the oil and gas from such wells is sold. The
Trust believes that it will continue to have revenues sufficient to permit
distributions to be made to unitholders for the foreseeable future, although no
assurance can be made regarding the amounts thereof. The foregoing sentence is a
forward-looking statement. Factors that might cause actual results to differ
from expected results include reductions in prices or demand for oil and gas,
which might then lead to decreased production; reductions in production due to
depletion of existing wells or disruptions in service, including as the result
of storm damage to production facilities, blowouts or other production
accidents, and geological changes such as cratering of productive formations;
expiration or release of leases subject to the Trust's interests; and the
discontinuation by parties subject to the contract dated April 30, 1951 between
the predecessors of Tidelands Royalty Trust "B" ("Tidelands") and Gulf Oil
Corporation of their efforts to obtain leases in the area that is subject to
Tidelands' interests.

                                        6
<PAGE>   8

     Important aspects of the Trust's operations are conducted by third parties.
These include the production and sale of oil and gas and the calculation and
payment of royalties to the Trust, which are conducted by oil and gas companies
that lease tracts subject to the Trust's interests. Similarly, the Trust's
distributions are processed and paid by the Bank of New York. Any disruption of
the Trust's operations that results from Year 2000 problems of these third
parties could have a material adverse effect on the Trust. The Trust does not
have access to information that would permit it to determine the status of
certain of these third parties' efforts to analyze and address Year 2000 issues.
The Trust is monitoring these parties' public announcements and disclosure
regarding Year 2000 issues, and has sought direct assurances where appropriate,
in an effort to ensure that these parties address Year 2000 issues that could
adversely affect the Trust.

RESULTS OF OPERATIONS -- THREE MONTHS ENDED SEPTEMBER 30, 1999

     Net income for the quarter ended September 30, 1999 amounted to $1,077,262
(including the $124,000 release of the accounts payable reserve) which was
approximately 57% more than the $685,780 (including the $130,000 release of the
accounts payable reserve) realized in the comparable period of 1998.

     Revenue from oil royalties, including the Trust's shares of Tidelands'
royalties increased 143% to $436,194 in the current quarter from $179,200
realized in the comparable period a year ago. As shown in the table below, the
increase in oil production over the comparable period a year ago was due to both
increased sales quantities and higher prices.

     Revenue from gas royalties, including the Trust's shares of Tidelands'
royalties increased 19% to $657,015 in the current quarter from $552,436 in the
comparable period a year ago. The gas revenue figures include the additional
revenue from the reduction of the accounts payable reserve as discussed above.
As shown in the table below, gas production decreased over the comparable period
a year ago, and there was an increase in natural gas prices.

     Income from the Trust's equity interest in Tidelands increased
approximately 79% in the current period over the comparable period last year due
to an increase in Tidelands' revenue from both oil and gas.

     The quantities of oil and gas sold and the average prices realized (from
current operations without the revenues realized from the reduction of the
accounts payable reserve as described above and including the Trust's equity in
Tidelands) for the three months ended September 30, 1999, and those realized in
the comparable 1998 quarter, are presented in the following table:

<TABLE>
<CAPTION>
                                                                1999        1998
                                                              --------    --------
<S>                                                           <C>         <C>
OIL
  Barrels sold..............................................    23,388      12,844
  Average price.............................................  $  18.65    $  13.95

NATURAL GAS
  Mcf sold..................................................   213,537     223,920
  Average price.............................................  $   2.50    $   1.89
</TABLE>

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

     Not applicable.

                                        7
<PAGE>   9

                           PART II. OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K

     (a) The following exhibits are included herein:

<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                             DESCRIPTION OF EXHIBIT
        -------                             ----------------------
<C>                      <S>
          27.1           -- Financial Data Schedule
</TABLE>

     (b) Current Reports on Form 8-K:

          None

                                        8
<PAGE>   10

                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                            MARINE PETROLEUM TRUST

                                            Bank of America, N.A., Trustee

November 15, 1999                           By:   /s/ CINDY STOVER MILLER
                                              ----------------------------------
                                                     Cindy Stover Miller
                                                        Vice President

November 15, 1999                                    /s/ R. RAY BELL
                                            ------------------------------------
                                                Principal Accounting Officer

                                        9
<PAGE>   11

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                             DESCRIPTION OF EXHIBIT
        -------                             ----------------------
<C>                      <S>
          27.1           -- Financial Data Schedule
</TABLE>