<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, 1997
                                       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>
<C>                                            <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, 1997
         ----------------------------              --------------------------------------
<C>                                            <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, 1997 AND JUNE 30, 1997
                                  (UNAUDITED)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                              DECEMBER 31,      JUNE 30,
                                                                  1997            1997
                                                              -------------    ----------
<S>                                                           <C>              <C>
Current Assets:
  Cash and cash equivalents.................................   $2,206,850      $1,759,718
  Oil and gas royalties receivable..........................      308,736         835,230
  Receivable from affiliate.................................      215,022          64,580
                                                               ----------      ----------
          Total current assets..............................    2,730,608       2,659,528
                                                               ----------      ----------
Investment in affiliate.....................................      290,730         285,478
Office equipment, at cost less accumulated depreciation.....        1,110             272
Producing oil and gas properties............................            7               7
                                                               ----------      ----------
                                                               $3,022,455      $2,945,285
                                                               ==========      ==========
 
                              LIABILITIES AND TRUST EQUITY
 
Current Liabilities:
  Accounts payable..........................................   $  895,724      $  895,724
  Income taxes payable......................................        4,458           4,758
                                                               ----------      ----------
          Total current liabilities.........................      900,182         900,482
Trust Equity:
  Corpus -- authorized 2,000,000 units of beneficial
     interest,
     issued 2,000,000 units at nominal value................            8               8
  Undistributed income......................................    2,122,265       2,044,795
                                                               ----------      ----------
          Total trust equity................................    2,122,273       2,044,803
                                                               ----------      ----------
                                                               $3,022,455      $2,945,285
                                                               ==========      ==========
</TABLE>
 
                                        2
<PAGE>   3
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                  CONDENSED CONSOLIDATED STATEMENTS OF INCOME
      FOR THE THREE MONTHS AND SIX MONTHS ENDED DECEMBER 31, 1997 AND 1996
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                  THREE MONTHS                SIX MONTHS
                                             ----------------------    ------------------------
                                               1997         1996          1997          1996
                                             --------    ----------    ----------    ----------
<S>                                          <C>         <C>           <C>           <C>
Income:
  Oil and gas royalties....................  $825,162    $1,085,760    $1,433,372    $1,946,771
  Equity in earnings of affiliate..........   133,285        79,284       250,232       150,696
  Interest income of subsidiary............    22,607        22,794        47,900        48,878
                                             --------    ----------    ----------    ----------
                                             $981,054    $1,187,838    $1,731,504    $2,146,345
                                             --------    ----------    ----------    ----------
Expenses:
  General and administrative...............    37,135        47,881        72,840        75,739
                                             --------    ----------    ----------    ----------
  Income before Federal income taxes.......   943,919     1,139,957     1,658,664     2,070,606
  Federal income taxes of subsidiary.......     3,300         2,500         5,700         5,500
                                             --------    ----------    ----------    ----------
          Net income.......................  $940,619    $1,137,457    $1,652,964    $2,065,106
                                             ========    ==========    ==========    ==========
Net income per unit........................  $   0.47    $     0.57    $     0.83    $     1.03
                                             ========    ==========    ==========    ==========
Distributions per unit.....................  $   0.35    $     0.49    $     0.79    $     0.99
                                             ========    ==========    ==========    ==========
</TABLE>
 
                                        3
<PAGE>   4
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
              FOR THE SIX MONTHS ENDED DECEMBER 31, 1997 AND 1996
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                 1997           1996
                                                              -----------    -----------
<S>                                                           <C>            <C>
Cash flows from operating activities:
  Net income................................................  $ 1,652,964    $ 2,065,106
  Adjustments to reconcile net income to net cash provided
     by operating activities:
     Depreciation...........................................        1,381            349
     Changes in assets and liabilities:
       Decrease (increase) in Royalties receivable..........      526,494       (136,590)
       Receivable from affiliate............................     (150,442)        23,311
       Employment tax payable...............................                        (324)
       Federal income taxes payable.........................         (300)         1,700
                                                              -----------    -----------
          Net cash provided by operating activities.........    2,030,097      1,953,552
                                                              -----------    -----------
Cash flows provided by (used in) investing activities:
       Purchase of office equipment.........................       (2,219)
       Decrease (increase) in undistributed earnings of
        affiliate...........................................       (5,252)        14,105
Cash flows from financing activities -- distributions to
  unitholders...............................................   (1,575,494)    (1,972,357)
                                                              -----------    -----------
          Net increase (decrease) in cash and cash
             equivalents....................................      447,132         (4,700)
                                                              -----------    -----------
Cash and cash equivalents at beginning of period............    1,759,718      2,020,695
                                                              -----------    -----------
Cash and cash equivalents at end of period..................  $ 2,206,850    $ 2,015,995
                                                              ===========    ===========
</TABLE>
 
                                        4
<PAGE>   5
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                               DECEMBER 31, 1997
                                  (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, 1997. 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, 1997 includes $1,410,194 applicable to
the Trust and $712,071 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
 
     Distributable income declined in each of the last four quarters due mainly
to a decrease in the production and sale of oil and gas. Oil production included
in distributable income declined to 184 barrels per day in the quarter ended
December 31, 1997 from 312 barrels per day in the quarter ended December 31,
1996. Likewise gas production included in distributable income declined to 1807
mcf per day in the quarter ended December 31, 1997 from 2889 mcf per day in the
quarter ended December 31, 1996. The following table compares the quarterly
distributable income per unit for the past two years.
 
<TABLE>
<CAPTION>
                          QUARTER                             1997     1996
                          -------                             -----    -----
<S>                                                           <C>      <C>
March 31....................................................  $ .52    $ .31
June 30.....................................................    .46      .40
September 30................................................    .44      .50
December 31.................................................    .35      .49
                                                              -----    -----
          Total for year....................................  $1.77    $1.70
                                                              =====    =====
</TABLE>
 
     Income from the Trust's 32.6% equity interest in Tidelands Royalty Trust B
increased 68% in the current quarter as compared to the comparable period last
year. Tidelands' income has increased as the result of new gas production on
Galveston Block 303.
 
     The Trust's current fiscal year began on July 1, 1997. Since that date,
operators have completed 17 new development wells on leases in which the Trust
has an interest. Seven of the wells were not successful or were abandoned, while
10 were completed as either oil or gas producers. At the present time operators
have 9 development wells in process and 8 locations for development wells to be
drilled in the future. The Trust understands that approximately half of the
wells are sidetracked out of existing wells that are no longer producing.
 
                                        6
<PAGE>   7
 
     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
Tidelands' predecessors and Gulf Oil Corporation of their efforts to obtain
leases in the area that is subject to Tidelands' interests.
 
RESULTS OF OPERATIONS -- THREE MONTHS ENDED DECEMBER 31, 1997
 
     Net income for the quarter ended December 31, 1997 amounted to $940,619,
which was approximately 17% less than the $1,137,457 realized in the comparable
period of 1996.
 
     The volume of oil sold decreased approximately 3% over the comparable
period last year, and the average price per barrel of oil decreased to $18.75
per barrel from $28.98 a year ago.
 
     Natural gas volumes sold decreased approximately 2% in the current period
from the comparable period last year. Natural gas volumes amounted to 241,932
mcf this period and were 248,056 mcf for the comparable period last year. The
average price increased $.08 to $2.50 per mcf, from $2.42 a year ago.
 
     Income from the equity interest in Tidelands increased approximately 68% in
the current period over the comparable period last year. See " -- General."
 
     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, 1997 and 1996 are presented in the following table:
 
<TABLE>
<CAPTION>
                                                                1997       1996
                                                              --------    -------
<S>                                                           <C>         <C>
OIL
  Barrels sold..............................................    18,946     19,584
  Average price.............................................  $  18.75    $ 28.98
 
NATURAL GAS
  Mcf sold..................................................   241,932    248,056
  Average price.............................................  $   2.50    $  2.42
</TABLE>
 
                                        7
<PAGE>   8
 
RESULTS OF OPERATIONS -- SIX MONTHS ENDED DECEMBER 31, 1997
 
     Net income for the six months ended December 31, 1997 amounted to
$1,652,964, which was approximately 20% less than the $2,065,106 realized in the
comparable period of 1996.
 
     The volume of oil sold decreased approximately 14% over the comparable
period last year, and the average price per barrel of oil (based on actual
receipts) decreased to $18.21 per barrel from $24.17 a year ago.
 
     Natural gas volumes sold decreased approximately 7% in the current period
from the comparable period last year. Natural gas volumes amounted to 424,991
mcf this period and were 457,024 mcf for the comparable period last year. The
average price increased $.07 to $2.40 per mcf, from $2.33 a year ago.
 
     Income from the equity interest in Tidelands increased approximately 66% in
the current period over the comparable period last year. 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,
1997 and 1996 are presented in the following table:
 
<TABLE>
<CAPTION>
                                                                1997        1996
                                                              --------    --------
<S>                                                           <C>         <C>
OIL
  Barrels sold..............................................    36,865      42,685
  Average price.............................................  $  18.21    $  24.17
 
NATURAL GAS
  Mcf sold..................................................   424,991     457,024
  Average price.............................................  $   2.40    $   2.33
</TABLE>
 
PART II. OTHER INFORMATION
 
     There were no events reportable under Part II of the Quarterly Report on
Form 10-Q.
 
                                        8
<PAGE>   9
 
                                   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 10, 1998                           By:      /s/ JANE J. SHEA
 
                                              ----------------------------------
                                                         Jane J. Shea
                                                        Vice President
 
February 10, 1998                                    /s/ R. RAY BELL
 
                                            ------------------------------------
                                                Principal Accounting Officer
 
                                        9
<PAGE>   10
                               INDEX TO EXHIBITS


<TABLE>
<CAPTION>
EXHIBIT
  NO.                   ITEM
-------                 ----
  <S>          <C>
  27           Financial Data Schedule
</TABLE>