<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 DECEMBER 31, 1995

                                      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.)

          NATIONSBANK OF TEXAS, 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                          DECEMBER 31, 1995
----------------------------------------       ----------------------------------------------
<S>                                               <C>
         Units of Beneficial Interest                           2,000,000
</TABLE>
 
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<PAGE>   2
 
PART I. FINANCIAL INFORMATION
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                     CONDENSED CONSOLIDATED BALANCE SHEETS
                      DECEMBER 31, 1995 AND JUNE 30, 1995
                                  (UNAUDITED)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                     DECEMBER 31,      JUNE 30,
                                                                         1995            1995
                                                                     ------------     ----------
<S>                                                                  <C>              <C>
Current Assets:
  Cash and cash equivalents........................................   $1,719,141      $1,661,312
  Oil and gas royalties receivable.................................      417,381         387,460
  Receivable from affiliate........................................       82,502          88,771
                                                                     -----------      ----------
          Total current assets.....................................    2,219,024       2,137,543
                                                                     -----------      ----------
Investment in affiliate............................................      237,093         199,226
Office equipment, at cost less accumulated depreciation............        1,322           1,672
Producing oil and gas properties...................................            7               7
                                                                     -----------      ----------
                                                                      $2,457,446      $2,338,448
                                                                     ===========      ==========
                          LIABILITIES AND TRUST EQUITY
Current Liabilities:
  Accounts payable.................................................   $  895,724      $  895,724
  Employment tax payable...........................................        1,377           3,836
  Income taxes payable.............................................        4,018           7,018
                                                                     -----------      ----------
          Total current liabilities................................      901,119         906,578
Trust Equity:
  Corpus -- authorized 2,000,000 units of beneficial interest,
     issued 2,000,000 units at nominal value.......................            8               8
  Undistributed income.............................................    1,556,319       1,431,862
                                                                     -----------      ----------
          Total trust equity.......................................    1,556,327       1,431,870
                                                                     -----------      ----------
                                                                      $2,457,446      $2,338,448
                                                                     ===========      ==========
</TABLE>
 
                                        2
<PAGE>   3
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                  CONDENSED CONSOLIDATED STATEMENTS OF INCOME
      FOR THE THREE MONTHS AND SIX MONTHS ENDED DECEMBER 31, 1995 AND 1994
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                   THREE MONTHS                 SIX MONTHS
                                               ---------------------     -------------------------
                                                 1995         1994          1995           1994
                                               --------     --------     ----------     ----------
<S>                                            <C>          <C>          <C>            <C>
Income:
  Oil and gas royalties......................  $543,819     $393,232     $1,079,625     $  847,797
  Equity in earnings of affiliate............    92,915       41,094        184,237        189,445
  Interest income of subsidiary..............    23,470       19,739         46,891         37,829
                                               --------     --------     ----------     ----------
                                               $660,204     $454,065     $1,310,753     $1,075,071
                                               --------     --------     ----------     ----------
Expenses:
  General and administrative.................    36,870       30,931         57,506         48,370
                                               --------     --------     ----------     ----------
  Income before Federal income taxes.........   623,334      423,134      1,253,247      1,026,701
  Federal income taxes of subsidiary.........        --        1,146             --          2,612
                                               --------     --------     ----------     ----------
  Net income.................................  $623,334     $421,988     $1,253,247     $1,024,089
                                               ========     ========     ==========     ==========
Net income per unit..........................  $    .31     $    .21     $      .63     $      .51
                                               ========     ========     ==========     ==========
Distributions per unit.......................  $    .29     $    .29     $      .56     $      .63
                                               ========     ========     ==========     ==========
</TABLE>
 
                                        3
<PAGE>   4
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
              FOR THE SIX MONTHS ENDED DECEMBER 31, 1995 AND 1994
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                       1995            1994
                                                                    -----------     -----------
<S>                                                                 <C>             <C>
Cash flows from operating activities:
  Net income......................................................  $ 1,253,247     $ 1,024,089
  Adjustments to reconcile net income to net cash provided by
     operating activities:
     Depreciation.................................................          350             421
     Change in assets and liabilities:
       Decrease (increase) in royalties receivable................      (29,921)         85,469
       Decrease (increase) in receivable from affiliate...........        6,269          39,619
     Increase (decrease) in employment tax payable................       (2,459)             --
     Increase (decrease) in Federal income taxes payable..........       (3,000)         (1,647)
                                                                    -----------     -----------
          Net cash provided by operating activities...............    1,224,486       1,147,951
                                                                    -----------     -----------
Cash flows provided by (used in) investing activities:
       Decrease (increase) in undistributed earnings of
        affiliate.................................................      (37,867)         17,785
                                                                    -----------     -----------
          Net cash provided by investing activities...............      (37,867)         17,785
                                                                    -----------     -----------
Cash flows from financing activities -- distributions
  unitholders.....................................................   (1,128,790)     (1,251,132)
                                                                    -----------     -----------
          Net increase (decrease) in cash and cash equivalents....       57,829         (85,396)
                                                                    -----------     -----------
Cash and cash equivalents at beginning of period..................    1,661,312       1,825,507
                                                                    -----------     -----------
Cash and cash equivalents at end of period........................  $ 1,719,141     $ 1,740,111
                                                                    ===========     ===========
</TABLE>
 
                                        4
<PAGE>   5
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                               DECEMBER 31, 1995
                                  (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 annual report for the fiscal year
ended June 30, 1995. 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.
 
UNDISTRIBUTED INCOME
 
     Undistributed income on December 31, 1995 includes $957,446 applicable to
the Trust and $598,873 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 $895,724 to
cover possible refunds that may be required upon redetermination of gas prices
for royalty payments in prior periods.
 
                                        5
<PAGE>   6
 
                    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
 
     Cash distributions to unitholders amounted to $.29 per unit for the current
quarter and $1.09 for the last four quarters. There is a one month time
difference between the production of oil and a two month time difference between
the production of gas and the receipt of royalties on that production. The
distribution for the current quarter included gas produced in September and oil
produced in October. Accordingly, any benefit to the Trust from increases in gas
prices that occurred after September 1995 would be realized in the first
quarterly distribution in 1996.
 
     Operators have been active in drilling and workover operations in several
of the fields in which Marine has an overriding royalty interest. The drilling
program in the Eugene Island Block 238 Field has resulted in a 226% increase in
revenue for the Trust from the oil and gas sold from that field in the current
quarter as compared to the comparable quarter last year. Over the past three
years Chevron has drilled and completed 10 new wells in the field.
 
     Since June 30, 1995, the end of the Trust's last fiscal year, operators
have commenced 10 new drilling operations, 7 of which have been completed as oil
or gas wells, 2 of which were dry holes, and 2 of which are not yet completed.
 
     The Trust's income from its equity interest in Tidelands Royalty Trust B
("Tidelands") was $.05 per unit in the 3 months and $.09 per unit in the six
months ended December 31, 1995. Approximately 95% of Tidelands' income is from
gas production. The majority of that production is from the West Cameron Block
165 Field, operated by Pennzoil, and the High Island Block 128 Field, operated
by Chevron. The three wells operated by Seneca Resources in the West Cameron
Block 229 Field are reported to be depleted. Gas production from these wells
commenced in November 1992 and was discontinued in October 1995. During the
period in which these wells were in production, they accounted for a significant
portion of the Trust's income. Income from these wells in the current quarter
was not significant.
 
RESULTS OF OPERATIONS -- THREE MONTHS ENDED DECEMBER 31, 1995
 
     Net income for the quarter ended December 31, 1995 amounted to $623,334,
which was approximately 48% more than the $421,988 realized in the comparable
period of 1994.
 
     The volume of oil sold increased approximately 29% over the comparable
period last year, and the average price per barrel of oil increased $1.39 to
$16.31 per bbl from $14.92 a year ago.
 
     Natural gas volumes sold increased approximately 27% in the current period
over the comparable period last year. Natural gas volumes amounted to 216,529
mcf this period and were 170,165 mcf for the comparable period last year. The
average price increased $.39 to $1.71 per mcf, from $1.32 a year ago.
 
     Marine's equity in the income of Tidelands increased approximately 126% in
the current period over the comparable period last year. See "-- General."
 
                                        6
<PAGE>   7
 
     The quantities of oil and gas sold and the average prices for oil and gas
(including the equity in Tidelands) for the three month periods ended December
31, 1995 and 1994 are presented in the following table:
 
<TABLE>
<CAPTION>
                                                                        1995        1994
                                                                       -------     -------
    <S>                                                                <C>         <C>
    OIL
      Barrels sold...................................................   18,193      14,132
      Average price..................................................   $16.31      $14.92
    NATURAL GAS
      mcf sold.......................................................  216,529     170,165
      Average price..................................................    $1.71       $1.32
</TABLE>
 
RESULTS OF OPERATIONS -- SIX MONTHS ENDED DECEMBER 31, 1995
 
     Net income for the six months ended December 31, 1995 amounted to
$1,253,247, which was approximately 22% more than the $1,024,089 realized in the
comparable period of 1994.
 
     The volume of oil sold in the current six-month period increased
approximately 27% over the comparable period in 1994, and there was an
approximately 3% increase in the average price received. The volume of natural
gas sold in the current period increased approximately 17% over the comparable
period in 1994 and the average price received for natural gas increased to $1.64
per mcf from the $1.52 received during the 1994 period.
 
     Income from the equity interest in Tidelands decreased approximately 3% in
the current six months as compared to the comparable period in 1994. Income from
this source in the six months ended December 31, 1994 amounted to $189,445, but
decreased to $184,237 in the current six months. See "-- General."
 
     The quantities of oil and gas sold and the average prices for oil and gas
(including the equity in Tidelands) for the six-month periods ended December 31,
1995 and 1994 are presented in the following table:
 
<TABLE>
<CAPTION>
                                                                         1995        1994
                                                                       --------    --------
    <S>                                                                <C>         <C>
    OIL
      Barrels sold...................................................    34,725      27,320
      Average price..................................................    $16.22      $15.77
    NATURAL GAS
      mcf sold.......................................................   427,161     364,207
      Average price..................................................     $1.64       $1.52
</TABLE>
 
PART II. OTHER INFORMATION
 
     There were no events reportable under Part II of the Quarterly Report on
Form 10-Q.
 
                                        7
<PAGE>   8
 
                                   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
 
                                            NationsBank of Texas, N.A., Trustee
 
February 12, 1996                           By:       /s/  PAT COX
                                                  ----------------------------
                                                  Pat Cox, Vice President
 
February 12, 1996                                   /s/  R. RAY BELL
                                             ---------------------------------
                                             R. Ray Bell, Principal Accounting
                                                          Officer
 
                                        8
<PAGE>   9
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
                                                                                   SEQUENTIAL
  EXHIBIT                                                                             PAGE
  NUMBER                            EXHIBIT DESCRIPTION                              NUMBER
----------                    ---------------------------------------------------  -----------
<S>                           <C>                                                  <C>
     27                          -- Financial Data Schedule
</TABLE>