<PAGE>   1
 
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                                   FORM 10-K
 
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
 
<TABLE>
<C>   <S>
[X]             FOR THE FISCAL YEAR ENDED JUNE 30, 1998

                                   OR

[ ]   FOR THE TRANSITION PERIOD FROM --------------- TO  ---------------.
COMMISSION FILE NO. 0-8565
</TABLE>
 
                             MARINE PETROLEUM TRUST
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                            <C>
                    TEXAS                                        75-6008017
       (State or other jurisdiction of                        (I.R.S. Employer
        incorporation or organization)                      Identification No.)
</TABLE>
 
                           C/O THE CORPORATE TRUSTEE:
                           NATIONSBANK OF TEXAS, N.A.
                   P.O. BOX 830241, DALLAS, TEXAS 75283-0241
              (Address of principal executive offices) (Zip Code)
 
               Registrant's telephone number, including area code
            (at the office of the Corporate Trustee): (800) 985-0794
 
          Securities registered pursuant to Section 12(b) of the Act:
 
                                      NONE
 
          Securities registered pursuant to Section 12(g) of the Act:
 
                          UNITS OF BENEFICIAL INTEREST
 
     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, and (2) has been subject to such filing
requirements for the past 90 days.
 
                                YES  X    NO 
                                    ---      ---
 
     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained, to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K.  [X]
 
     Aggregate market value of Units of Beneficial Interest held by
non-affiliates of the registrant at August 14, 1998: $25,716,167.
 
     Number of Units of Beneficial Interest outstanding as of the close of the
period covered by this report: June 30, 1998 -- 2,000,000 Units.
 
                      Documents Incorporated by Reference:
 
                                      NONE
 
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<PAGE>   2
 
                             CROSS-REFERENCE SHEET
 
     This Form 10-K for the year ended June 30, 1998 of Marine Petroleum Trust
is not organized by conventional item numbers and headings contemplated by SEC
rules and forms. This cross-reference page is intended to indicate to the reader
where (or under which headings) information required under Form 10-K may be
found herein.
 
<TABLE>
<CAPTION>
 FORM 10-K                                                            HEADINGS
ITEM NUMBERS                                                           HEREIN
------------                                                          --------
<S>         <C>                                               <C>
PART I......................................................  General
  Item  1.  Business........................................  The Trust; Properties
  Item  2.  Properties......................................  Properties
  Item  3.  Legal Proceedings...............................  Legal Matters
  Item  4.  Submission of Matters to a Vote of Security
              Holders.......................................  Unitholder Voting Matters
PART II.....................................................  Financial
  Item  5.  Market for Registrant's Common Equity and
              Related Stockholder Matters...................  Market and Investor Information
  Item  6.  Selected Financial Data.........................  Selected Financial Data
  Item  7.  Management's Discussion and Analysis of
              Financial Condition and Results of
              Operations....................................  Management's Discussion and Analysis of
                                                                Financial Condition and Results of
                                                                Operations
  Item  8.  Financial Statements and Supplementary Data.....  Financial Statements and Supplementary
                                                                Data
  Item  9.  Disagreements on Accounting and Financial
              Disclosure....................................  Accounting Matters
PART III....................................................  Management and Principal Unitholders
  Item 10.  Directors and Executive Officers of the
              Registrant....................................  Administrators
  Item 11.  Management Remuneration.........................  Administrators; Management Compensation
  Item 12.  Security Ownership of Certain Beneficial Owners
              and Management................................  Principal Unitholders
  Item 13.  Certain Relationships and Related
              Transactions..................................  Administrators; Management Compensation
PART IV.....................................................  Miscellaneous
  Item 14.  Exhibits, Financial Statement Schedules and
              Reports on Form 8-K...........................  Exhibits, Financial Statement Schedules
                                                                and Reports on Form 8-K
</TABLE>
<PAGE>   3
 
                                    GENERAL
 
                                   THE TRUST
 
     Organization. Marine Petroleum Trust ("Marine") is a royalty trust created
in 1956 under the laws of the State of Texas. Marine is not permitted to engage
in any business activity inasmuch as it was organized for the sole purpose of
providing an efficient, orderly, and practical means for the administration and
liquidation of rights to payments from certain oil and gas leases in the Gulf of
Mexico, pursuant to license agreements and amendments thereto between Marine's
predecessors and Gulf Oil Corporation ("Gulf"). As a result of various
transactions that have occurred since 1956, the Gulf interests now are held by
Chevron Corporation ("Chevron"), Elf Acquitane, Inc. ("Elf"), and their
assignees.
 
     The indenture pursuant to which Marine was created (the "Indenture"),
provides that the corporate trustee is to distribute all cash in Marine, less an
amount reserved for the payment of accrued liabilities and estimated future
expenses, to unitholders of record on the 28th day of September, December, March
and June of each fiscal year. If the 28th falls on a Saturday, Sunday or legal
holiday, the distribution is payable on the immediately preceding business day.
 
     The Indenture also provides that the term of the royalty trust created
thereby will expire on June 1, 2001 unless extended by the vote of the holders
of a majority of the outstanding units of beneficial interest. See "Unitholder
Voting Matters."
 
     Marine's wholly-owned subsidiary, Marine Petroleum Corporation ("MPC"),
holds title to interests in properties subject to Marine's interests that are
situated offshore of Louisiana. Ninety-eight percent of all oil, gas, and other
mineral royalties collected by this subsidiary are paid to Marine. MPC, like
Marine, is prohibited from engaging in a trade or business and does only those
things necessary for the administration and liquidation of its properties.
 
     Marine's only industry segment or purpose is the administration and
collection of royalties.
 
     Royalties. Marine's rights are generally referred to as overriding royalty
interests in the oil and gas industry, and are sometimes referred to herein as
such. All production and marketing functions are conducted by the working
interest owners of the leases. Revenues from the overriding royalties are paid
to Marine either (i) on the basis of the selling price of oil, gas and other
minerals produced, saved and sold, or (ii) at the value at the wellhead as
determined by industry standards, when the selling price does not reflect the
value at the wellhead.
 
     The contracts creating these interests were entered into between
predecessors of Marine and Gulf, and relate to two different types of interests.
One type of interest is an overriding royalty interest equal to three-fourths of
1% of the value at the well of any oil, gas, or other minerals produced and
sold. Marine's overriding royalty interest applies only to existing leases and
does not apply to new leases. The second interest is Marine's 32.6% equity
interest in Tidelands Royalty Trust "B" ("Tidelands"), a separate Texas trust,
which owns similar interests in any oil, gas, or other mineral lease acquired by
Gulf and/or its transferees and assignees in a 1,370,000-acre area (divided into
60 tracts) of the Gulf of Mexico during a 50-year period ending April 30, 2001.
Tidelands' interest in each tract consists of (i) a production payment, which
reverts to an overriding royalty, on oil and gas and (ii) an overriding royalty
on other minerals. The production payment is payable out of 12.5% of the value
at the well of oil and gas produced and sold from leases on a subject tract
until Tidelands has earned $1,500,000 on such tract. The production payment then
reverts to an overriding royalty interest equal to approximately 4.17% of the
value at the well of oil and gas sold from the tract. Tidelands' overriding
royalty interest on minerals other than oil and gas is payable at the rate of
4.17% of the value of such minerals sold from the property. Marine, through its
ownership of units of beneficial interest in Tidelands, derives a 32.6% interest
in the production payments and overriding royalties of Tidelands.
 
     Presently, the leases subject to Marine's interests cover 281,976 gross
acres (including Tidelands' interest in 31,375 leased acres). These leases will
remain in force until the expiration of their respective terms. Leases may be
voluntarily released by the working interest owner after all oil and gas
reserves are produced. They may also be abandoned by the working interest owner
due to failure to discover sufficient reserves to make development economically
worthwhile. In addition, the federal government may force termination if the
working interest owner fails to fully develop a lease once it is acquired.
<PAGE>   4
 
     For the year ended June 30, 1998, approximately 37% of Marine's royalty
revenues were attributable to the sale of oil and approximately 63% were
attributable to the sale of natural gas. The royalty revenues received by Marine
are affected by seasonal fluctuations in demand. Royalty revenue received by
Marine from Chevron and from Pennzoil Exploration and Production Company
("Pennzoil") accounted in the aggregate for approximately 85%, 81% and 88% of
Marine's royalty revenue for the years ended June 30, 1998, 1997 and 1996,
respectively. In addition, Marine's revenue from its equity interest in
Tidelands accounted for approximately 15%, 8% and 12% of Marine's revenue for
the years ended June 30, 1998, 1997 and 1996, respectively. Tidelands has
reported that royalty revenues from Burlington Resources, Chevron and Pennzoil
accounted for a substantial portion of Tidelands' royalty revenue for the years
ended December 31, 1997, 1996 and 1995.
 
     Marine derives no revenues from foreign sources and has no export sales.
 
     Trust Functions. Marine is administered by officers and employees of its
Trustee, NationsBank, N.A. MPC employs one individual (its president, treasurer
and director) to perform certain management, financial and administrative
services for Marine. Except for this individual, all officers and directors of
MPC serve without compensation. See "Management and Principal Unitholders."
 
     MPC leases office space in Dallas, Texas to provide work space and record
storage for Marine, MPC, Tidelands and Tidelands' wholly-owned subsidiary
corporation, Tidelands Royalty "B" Corporation. The cost of this office facility
is shared by all four of these entities in proportion to each entity's gross
income to the total of such income of all entities.
 
     The ability of Marine to receive revenues is entirely dependent upon its
entitlement to its rights with respect to the leases held by Chevron and its
assignees in the Gulf of Mexico (as more fully described in "Properties" below).
Moreover, no revenues are payable to Marine until sales of production commence
from any such lease.
 
     The royalty interests held by Marine are depleting with each barrel of oil
and mcf of natural gas produced. No funds are reinvested by Marine; thus, these
depleting assets are not being replaced.
 
                                   PROPERTIES
 
     General. Marine is not engaged in oil and gas operations, although its
income is based upon such operations of others. Marine's income is derived from
contracts that provide for payments in the nature of overriding royalties made
to Marine based on oil and gas sales from certain leases in the Gulf of Mexico.
 
     Reserves. Marine is not engaged in the production of crude oil or natural
gas. Its income is derived from overriding royalty payments which are carved out
of working interests in oil and gas leases in the Gulf of Mexico. Marine does
not have the engineering data necessary to make an estimate of proved oil and
gas reserves (nor the present value of future net cash flows from such
reserves), and is not entitled to receive such data from the owners of the
working interests from which Marine's interest is derived. See also "Difficulty
in Obtaining Certain Data" below.
 
     Since Marine does not have access to this reserve information, Marine is
unable to compute the standardized measure of discounted future net cash flows
therefrom.
 
     Marine did not file any reports during the fiscal year ended June 30, 1998
with any federal authority or agency with respect to oil and gas reserves.
 
                                        2
<PAGE>   5
 
     Production. Information regarding the net quantities of oil and gas
produced with respect to Marine's interests (including its equity in Tidelands)
for each of the last three fiscal years as well as the average sales price per
unit of oil and gas produced, upon which payments to Marine are based, is set
forth in the following table:
 
<TABLE>
<CAPTION>
                                                             YEAR ENDED JUNE 30,
                                                        -----------------------------
                                                         1998       1997       1996
                                                        -------    -------    -------
<S>                                                     <C>        <C>        <C>
Quantity
  Oil (in barrels ("bbls"))...........................   62,588     74,556     79,536
  Gas (in thousand cubic feet ("mcf"))................  754,143    997,454    876,055
Average Price
  Oil (per bbl.)......................................   $15.72     $21.31     $17.76
  Gas (per mcf).......................................    $2.74      $2.39      $2.08
</TABLE>
 
     Information about average production cost (lifting cost) per unit of
production has been omitted due to its unavailability and inapplicability to
Marine. For more recent information regarding crude oil sales prices, see
"Management's Discussion and Analysis of Financial Condition and Results of
Operations" below.
 
     Productive Wells. Based on the latest information available to Marine and
including its equity interest in Tidelands, there were approximately 306 wells
subject to Marine's interests actually producing at some time in calendar 1997,
some of which contained multiple completions. During calendar 1997,
approximately 134 wells produced oil and approximately 172 wells produced gas.
Most of the oil wells also produced associated gas and most of the gas wells
produced condensate, which is economically the equivalent of oil. See
"Difficulty in Obtaining Certain Data" below.
 
     Drilling Activity. Information concerning wells drilled and completed in
which Marine had an interest (including its equity interest in Tidelands) for
each of its last three fiscal years is set forth below:
 
                                WELLS COMPLETED
 
<TABLE>
<CAPTION>
                                                              YEAR ENDED JUNE 30,
                                                              --------------------
                                                              1998    1997    1996
                                                              ----    ----    ----
<S>                                                           <C>     <C>     <C>
Development
  Oil.......................................................    7       1       2
  Gas.......................................................    8       6       5
  Suspended*................................................   13      18      18
  Dry.......................................................    7       4       3
                                                               --      --      --
       Totals...............................................   35      29      28
                                                               ==      ==      ==
</TABLE>
 
---------------
 
* "Suspended" wells are completed wells the classification of which had not been
  reported at the relevant date.
 
     Information regarding net wells or acres is not included since Marine does
not own any working interests.
 
     Lease Acreage. Marine has an overriding royalty interest (including by
virtue of its equity interest in Tidelands) in 74 different oil and gas leases
covering 281,976 gross acres. These leases are located in the Central and
Western areas of the Gulf of Mexico off the coasts of Louisiana and Texas. This
acreage has been classified according to its current stage of development and is
presented in the following table:
 
<TABLE>
<CAPTION>
                                                            ACREAGE CLASSIFICATION
                                                 ---------------------------------------------
              LEASES GRANTED BY:                 PRODUCING   DEVELOPMENTAL(1)   EXPLORATORY(2)
              ------------------                 ---------   ----------------   --------------
<S>                                              <C>         <C>                <C>
United States..................................   276,446            0              8,231
State of Texas.................................       640            0                  0
State of Louisiana.............................     4,890            0                  0
                                                  -------           --              -----
                                                  281,976            0              8,231
                                                  =======           ==              =====
</TABLE>
 
                                        3
<PAGE>   6
 
---------------
 
(1) By definition, "Developmental Acreage" may be expected to produce royalty
    income at some point in the future.
 
(2) Leases are typically granted for a term of five years, during which the
    lease owner must establish a commercial production capability, or the lease
    expires. No commercial production has been established on the acreage
    classified above by Marine under the column heading "Exploratory." By
    definition, this acreage includes undrilled wildcat acreage as well as some
    possible discoveries which are awaiting further testing. The 8,231 acres are
    located on leases that have commercial production, but the production is not
    on Marine's overriding royalty area within those leases.
 
The overriding royalty interest owned by Marine is a fractional interest out of
total oil and gas sold, and is free and clear of all operating costs. The actual
percentage interest in a lease attributable to Marine's interest varies from
lease to lease. The acreage weighted average percentage interest attributable to
Marine's interest in all of these leases is .5905%.
 
     Present Activities. Published reports indicate that 9 wells are being
drilled on tracts in which Marine has an interest. Marine also understands from
published reports that plans are being made to begin drilling on 8 additional
wells.
 
     The U.S. Department of the Interior conducted a lease sale for the Gulf of
Mexico in April and August, 1998. Chevron did not bid on any tracts included in
this sale that are located in the 1,370,000 acre area subject to the Tidelands
contract (in which Marine has a 32.6% equity interest.)
 
     Difficulty in Obtaining Certain Data. Marine's only activities are the
collection and distribution of revenues from overriding royalties on certain oil
and gas leases in the Gulf of Mexico, pursuant to purchase agreements between
Marine's predecessors and Gulf and its transferees. The leasehold working
interests which are subject to the rights held by Marine are owned, in most
cases, in whole or in part by Chevron, or other oil and gas exploration and
production companies. Certain information as to reserves, availability of oil
and gas, average production cost (lifting cost) per unit, undeveloped acreage,
net wells and net acres, etc., with respect to the particular leases subject to
Marine's interests lies solely within the knowledge of these concerns.
Engineering data, if any, regarding these leaseholds would have been compiled
principally by or for the working interest owners of these leaseholds and Marine
believes that it will not be provided access to such information. Because of
this, it appears that unreasonable efforts and expense would be involved in
seeking to obtain all of the information required under Item 102 of Regulation
S-K and Securities Exchange Act of 1934 Industry Guide 2.
 
                                 LEGAL MATTERS
 
     Neither Marine nor MPC, nor any of their respective properties (exclusive
of properties owned by Chevron and subject to the Marine and Tidelands license
agreements), is a party to or subject to any material pending litigation as of
the date hereof.
 
                           UNITHOLDER VOTING MATTERS
 
     No matter was submitted by Marine during the year ended June 30, 1998 to a
vote of unitholders, whether through the solicitation of proxies or otherwise.
 
     Unitholders owning ten percent (10%) or more of the outstanding units may
at any time direct the Trustee to conduct an investigation to determine whether
the Trustee is receiving all revenues properly accruing to Marine's trust
estate. The Trustee may be removed by unitholders owning a majority of the
outstanding units. The unitholders owning eighty percent (80%) of the
outstanding units may amend and modify the Trust Indenture or any contract,
agreement or undertaking which constitutes a part of the trust estate, but no
such amendment may change the nature of the trust from that of a purely
ministerial trust, nor can there be any change in the rights or responsibilities
of the Trustee without its consent. However, no such change shall be made with
respect to any amendment to the Indenture if the Trustee shall receive written
 
                                        4
<PAGE>   7
 
objection from any unitholder within 20 days from the date of mailing to the
unitholders of the first notice of the proposed consent. Each unitholder has the
right to examine, inspect and audit all records relating to the trust estate.
 
     Marine is to continue until June 1, 2001, or until such later date as
holders of the units owning a majority of the outstanding units may designate,
but in any event, not more than 20 years from such designation. Alternatively,
instead of so extending the term of Marine, the holders of the units owning a
majority of the outstanding units may direct the Trustee to create one or more
corporations to receive and hold the trust estate, or any portion thereof,
unless the Trustee shall have received written objection from any unitholder
within 20 days from the date of mailing to the unitholders of the first notice
of the proposed consent. However, the unitholders owning eighty percent (80%) of
the outstanding units may terminate the trust on any date, whether earlier or
later than any such date determined as above, as they may specify.
 
     Upon termination of the trust (other than by the transfer of all the trust
estate to a corporation pursuant to the provisions of the Indenture, as
described above), the Trustee, after paying all of the obligations of the trust,
shall transfer to an agent appointed by the holders of the units owning a
majority of the outstanding units, by recordable assignments but without
warranty, the interests in the trust estate. Prior to termination of the trust,
no unitholder shall have any legal title in or to any of the properties
comprising the trust estate nor the right to secure any partition thereof.
 
                                   FINANCIAL
 
                        MARKET AND INVESTOR INFORMATION
 
     The units of beneficial interest in Marine trade on the Nasdaq SmallCap
Market under the symbol MARPS. Distributions of cash are made to unitholders
quarterly. The following table presents the range of high and low trade prices
by quarter for the past two years as reported by Nasdaq Online. The per unit
amount of cash distributed to unitholders for each of these quarters is also
presented in the table.
 
<TABLE>
<CAPTION>
                                                         TRADE PRICE
                                                      ------------------    DISTRIBUTIONS
                   QUARTER ENDING                      HIGH        LOW        PER UNIT
                   --------------                     -------    -------    -------------
<S>                                                   <C>        <C>        <C>
September 30, 1996..................................   14.000     10.250         .496
December 31, 1996...................................   16.250     12.750         .490
March 31, 1997......................................   17.500     14.750         .520
June 30, 1997.......................................   18.000     14.000         .464
September 30, 1997..................................   21.125     15.250         .437
December 31, 1997...................................   20.625     16.500         .351
March 31, 1998......................................   18.500     17.000         .511
June 30, 1998.......................................   19.500     17.250         .310
</TABLE>
 
     Marine is authorized to issue and has issued 2,000,000 units of beneficial
interest. On March 9, 1998, these outstanding units were held of record by 798
unitholders.
 
     During the first half of 1998, Marine received notice from The Nasdaq
SmallCap Market that Marine's units of beneficial interest would be delisted
because Marine did not satisfy Nasdaq's audit committee requirement. Marine
believes that its failure to satisfy this requirement is due to Marine's
organizational structure as a trust, which is managed by a trustee rather than
by a board of directors. On July 30, 1998, Marine appealed this determination in
an oral presentation to a Nasdaq hearing board. Representatives of the The
Nasdaq SmallCap Market advised Marine that the units of beneficial interest
would not be delisted and such units have continued to trade on The Nasdaq
SmallCap Market. Marine has not yet received a final written determination from
the appeal board, but believes that there will be no change in the status of
trading in the units of beneficial interest.
 
                                        5
<PAGE>   8
 
                            SELECTED FINANCIAL DATA
 
<TABLE>
<CAPTION>
                                                    (IN THOUSANDS EXCEPT PER UNIT AMOUNTS)
                                                ----------------------------------------------
                                                 1998      1997      1996      1995      1994
                                                ------    ------    ------    ------    ------
<S>                                             <C>       <C>       <C>       <C>       <C>
STATEMENT OF INCOME AND UNDISTRIBUTED INCOME
  SELECTED DATA
  Income:
     Oil and gas royalties....................  $2,577    $3,645    $2,842    $1,857    $2,044
     Equity in Tidelands......................     461       319       385       320     1,156
     Interest.................................     100       101        92        83        51
                                                ------    ------    ------    ------    ------
                                                $3,138    $4,065    $3,319    $2,260    $3,251
                                                ------    ------    ------    ------    ------
  Expenses:
     Taxes other than income..................  $    0    $    0    $    0    $    0    $    1
     General and administrative...............     146       143       121       118       106
     Federal income taxes.....................      12         8        12         6         3
                                                ------    ------    ------    ------    ------
                                                $  158    $  151    $  133    $  124    $  110
                                                ------    ------    ------    ------    ------
     Net income...............................  $2,980    $3,914    $3,186    $2,136    $3,141
                                                ======    ======    ======    ======    ======
     Distributions............................  $3,216    $3,939    $2,548    $2,287    $3,329
                                                ======    ======    ======    ======    ======
  Per Unit (2,000,000 outstanding)
     Net income...............................  $ 1.49    $ 1.96    $ 1.59    $ 1.07    $ 1.57
                                                ======    ======    ======    ======    ======
     Distributions............................  $ 1.61    $ 1.97    $ 1.27    $ 1.14    $ 1.66
                                                ======    ======    ======    ======    ======
BALANCE SHEET SELECTED DATA
  Total assets................................  $2,745    $2,945    $2,979    $2,338    $2,489
                                                ======    ======    ======    ======    ======
  Trust equity................................  $1,809    $2,045    $2,070    $1,432    $1,583
                                                ======    ======    ======    ======    ======
</TABLE>
 
                                        6
<PAGE>   9
 
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS
 
     Capital Resources and Liquidity. Because of the nature of Marine as a trust
entity, there is no requirement for capital; its only obligation is to
distribute to unitholders the net income actually collected. As an administrator
of oil and gas royalty properties, Marine collects income monthly, pays expenses
of administration, and disburses all net income collected to its unitholders
each quarter.
 
     Marine's Indenture (and the charter and by-laws of MPC) expressly prohibits
the operation of any kind of trade or business. Marine's oil and gas properties
are depleting assets and are not being replaced due to the prohibition against
these investments. These restrictions, along with other factors, allow Marine to
be treated as a grantor trust; thus all income and deductions, for tax purposes,
should flow through to each individual unitholder. Marine is not a taxable
entity.
 
     Results of Operations. Marine's income consists primarily of oil and gas
royalties and is based on the value at the well of its percentage interest in
oil and gas sold without reduction for any of the expense of production. Value
at the well for oil is the purchasers' posted price at its receiving point
onshore, less the cost of transportation from the offshore lease to the onshore
receiving point. In general, value at the well is determined on the basis of the
selling price of oil, gas and other minerals produced, saved and sold, or at
wellhead prices determined by industry standards, where the selling price does
not reflect value at the well.
 
     Summary Review. Marine's net income for the year ended June 30, 1998
amounted to $2,980,458 ($1.49 per unit) as compared to $3,914,197 ($1.96 per
unit) in the previous year. The 24% decrease resulted from a combination of
lower oil and gas production and lower prices for oil. Oil production was down
approximately 16% and gas production was down approximately 24%. The average
price received for oil dropped from $21.31 in fiscal 1997 to $15.72 in the
current fiscal year. The average price for gas increased to $2.74 in the current
fiscal year from $2.39 realized in fiscal 1997.
 
     Income from Marine's equity interest in Tidelands amounted to $461,095 in
the current fiscal year and in the previous year it was $319,251. Income from
Tidelands contributed approximately 15% of Marine's net income for the current
year. New gas production added in the third quarter of 1997 increased Tidelands'
income. Marine owns 452,366 units of beneficial interest in Tidelands
(32.6294%).
 
     During the current year the working interest owners on leases in which
Marine has an interest have drilled 35 new wells, consisting of seven oil wells,
eight gas wells, 13 wells on which operations were suspended and seven dry
holes. Available information indicates that the suspended wells will produce
either oil or gas. All of the wells were located in areas offshore from the
State of Louisiana. In addition to the 35 wells mentioned above, 24 wells were
recompleted to produce in different formations.
 
     The most recent data regarding producing wells available to Marine covers
production for the calendar year 1997. In that year there were 134 oil wells and
172 gas wells producing at some time during the year on leases in which Marine
has an interest. A number of the wells (approximately 38%) were first brought on
stream prior to 1990. However, approximately 81% of the oil and approximately
70% of the gas produced in 1997 was from wells that are from one to five years
old.
 
                                        7
<PAGE>   10
 
     The following table shows the royalty income, the net quantities sold, and
the average price received for oil and gas during the past three years
(including Marine's equity interest in Tidelands):
 
<TABLE>
<CAPTION>
                                                         FOR YEARS ENDED JUNE 30
                                                   ------------------------------------
                                                      1998         1997         1996
                                                   ----------   ----------   ----------
<S>                                                <C>          <C>          <C>
Income from
  Oil royalties..................................  $  983,978   $1,588,476   $1,412,750
  Gas royalties..................................   2,068,912    2,379,437    1,819,807
                                                   ----------   ----------   ----------
          Totals.................................  $3,052,890   $3,967,913   $3,232,557
                                                   ----------   ----------   ----------
Net quantities sold
  Oil (bbls).....................................      62,588       74,556       79,536
  Gas (mcf)......................................     754,143      997,454      876,055
Average price
  Oil............................................      $15.72       $21.31       $17.76
  Gas............................................        2.74         2.39         2.08
</TABLE>
 
     Marine's revenues are derived from the oil and gas production activities of
unrelated parties. Marine's revenues and distributions fluctuate from period to
period based upon factors beyond Marine's control, including without limitation
the number of leases bid on and obtained by parties subject to Marine's
interests, the number of productive wells drilled on leases subject to Marine's
interests, the level of production over time from such wells and the prices at
which the oil and gas from such wells is sold. Marine 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, blowouts or other production accidents, and geological changes such as
cratering of productive formations; expiration or release of leases subject to
Marine's interests; and the discontinuation by parties subject to Marine's
interests of their efforts to obtain leases in the Royalty Area.
 
     Marine's business consists solely of the collection of royalty payments,
the payment of expenses and the distribution of remaining amounts to
unitholders. Marine (through its subsidiary, Marine Petroleum Corporation) owns
only one personal computer, which is used by Marine for certain accounting and
general business functions. Marine believes that the computer and the software
used thereon are Year 2000 compliant. Marine also believes that Marine does not
own or lease any other assets containing imbedded computer chips, the failure of
which would have a material adverse effect on Marine.
 
     Important aspects of Marine's operations are conducted by third parties.
These include the production and sale of oil and gas and the calculation and
payment of royalty payments to Marine, which are conducted by oil and gas
companies that lease tracts subject to Marine's interests. Similarly, Marine's
distributions are processed and paid by The Bank of New York as the agent for
the trustee of Marine. Any disruption of Marine's operations that results from
Year 2000 problems of these third parties could have a material adverse effect
on Marine. Marine does not have access to information that would permit Marine
to determine the status of these third parties' efforts to analyze and address
Year 2000 issues. Marine intends to monitor these parties' public announcements
and disclosure regarding Year 2000 issues, and to seek direct assurances where
appropriate, in an effort to ensure that these parties address Year 2000 issues
that could adversely affect Marine.
 
     Marine's subsidiary, Marine Petroleum Corporation, has provided an account
payable of $758,250 to cover possible refunds that may be required upon
redetermination of gas prices for royalty payments in prior periods. During the
most recent fiscal year, Marine Petroleum Corporation determined that $137,474
of the previously-established account payable for possible royalty overpayments
no longer was required. Accordingly, during the most recent fiscal year, Marine
Petroleum Corporation reduced accounts payable, and increased net income by such
amount.
 
                                        8
<PAGE>   11
 
     During the most recent fiscal year, Chevron requested repayment for certain
royalties that Chevron believes Chevron incorrectly paid to Marine Petroleum
Corporation during 1995, 1996 and 1997. Marine Petroleum Corporation established
a reserve of $167,000 to cover this potential liability. In August of 1998,
Marine Petroleum Corporation repaid $157,000 to Chevron.
 
     Oil and Gas Royalties  -- 1998 and 1997: During fiscal 1998, Marine
received approximately 37% of its royalty income from the sale of oil and 63%
from the sale of natural gas. Income from such oil and gas royalties in fiscal
1998 decreased approximately 29% from fiscal 1997.
 
     Oil royalties, exclusive of Marine's interest in Tidelands, during fiscal
1998 ($947,656) were 39% less than oil royalties received in fiscal 1997
($1,544,131), due to a decrease in the quantity of oil sold and a decrease in
the average price received for oil sold.
 
     Natural gas royalties, exclusive of Marine's interest in Tidelands, during
fiscal 1998 ($1,629,470) were 22% lower than natural gas royalties received in
fiscal 1997 ($2,100,873). The decrease was due to the combination of a decrease
in the quantity of natural gas sold and an increase in the price received.
 
     Interest Income -- 1997 and 1998. Marine's interest income during fiscal
1998 decreased to $99,915 from the $100,705 earned in fiscal 1997, due primarily
to a decrease in funds invested.
 
     Equity in Tidelands -- 1997 and 1998. Marine realized income of $461,095
during fiscal 1998 from its interest in Tidelands, an increase of 44% from the
$319,251 earned in fiscal 1997.
 
     Oil and Gas Royalties -- 1996 and 1997: During fiscal 1997, Marine
received, exclusive of its interest in Tidelands, 42% of its royalty income from
the sale of oil and 58% from the sale of natural gas. Income from such oil and
gas royalties in fiscal 1997 increased 28% from fiscal 1996.
 
     Oil royalties, exclusive of Marine's interest in Tidelands, during fiscal
1997 ($1,544,131) were 12% more than oil royalties received in fiscal 1996
($1,375,880).
 
     Natural gas royalties, exclusive of Marine's interest in Tidelands, during
fiscal 1997 ($2,100,873) were 43% more than natural gas royalties received in
fiscal 1996 ($1,465,668).
 
     Interest Income -- 1996 and 1997. Marine's interest income increased 9%
during fiscal 1997 to $100,705 from the $92,275 earned in fiscal 1996, due
primarily to an increase in invested funds held for distribution.
 
     Equity in Tidelands -- 1996 and 1997. Marine owns beneficially 32.6% of the
outstanding units of beneficial interest in Tidelands. In fiscal 1997, Marine
realized income of $319,251 from its interest in Tidelands, a decrease of 17%
from the $384,753 earned in fiscal 1996.
 
     Pursuant to Tidelands' agreement with Chevron (as successor to Gulf's
interests), should Chevron acquire a lease or leases on any specified tracts in
the Gulf of Mexico before April 30, 2001, and oil or gas is produced or sold,
Chevron will make production payments to Tidelands in an amount equal to 12.5%
of the value of the oil and gas sold until the sum of $1,500,000 has been paid
on the tract. Thereafter, Tidelands' interest will be converted to an overriding
royalty and such payments will equal 4.17% of the value of the oil and gas sold
as long as the lease exists.
 
                                        9
<PAGE>   12
 
                  FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA
 
     The financial statements listed in the following Index, together with the
related notes and the report of KPMG Peat Marwick LLP, independent certified
public accountants, are presented on pages 11 through 18 hereof.
 
<TABLE>
<CAPTION>
                                                              PAGE
                                                              ----
<S>                                                           <C>
Independent Auditors' Report................................   12
Financial Statements:
  Consolidated Balance Sheets as of June 30, 1998 and
     1997...................................................   13
  Consolidated Statements of Income and Undistributed Income
     for the Three Years Ended June 30, 1998................   14
  Consolidated Statements of Cash Flows for
     the Three Years Ended June 30, 1998....................   15
  Notes to Consolidated Financial Statements................   16
</TABLE>
 
     See also "Exhibits, Financial Statement Schedules and Reports on Form 8-K"
of this Form 10-K for further information concerning the financial statements of
Marine and its subsidiaries.
 
     All schedules have been omitted for the reason that they are either not
required, not applicable or the required information is included in the
financial statements and notes thereto.
 
                               ACCOUNTING MATTERS
 
     During fiscal 1998 and 1997, there have been no disagreements between
Marine and its independent auditors on accounting or financial disclosure
matters which would warrant disclosure under Item 304 of Regulation S-K.
 
                      MANAGEMENT AND PRINCIPAL UNITHOLDERS
 
                                 ADMINISTRATORS
 
     Marine is a trust created under the laws of the State of Texas. Marine's
Indenture does not provide for directors or officers or the election of
directors or officers. Under the Indenture, NationsBank of Texas, N.A., serves
as Trustee.
 
     R. Ray Bell may be considered a significant employee of Marine. Mr. Bell
has been involved in the administration of Marine since its inception. He was
the chief financial officer of Marine's predecessor and is a certified public
accountant. Mr. Bell, 71 years old, is a graduate of Midwestern State University
of Wichita Falls, Texas with a Bachelor of Science degree in business
administration and economics. Since July 1, 1977, he has served as an officer
and director of MPC, and will continue to serve in such capacities until the
next meeting of directors and shareholders, respectively, of MPC or until his
successors are elected and qualified.
 
                                       10
<PAGE>   13
 
                            MANAGEMENT COMPENSATION
 
     During the fiscal year ended June 30, 1998, Marine paid or accrued fees of
$14,126 to NationsBank of Texas, N.A., as Trustee. These fees were paid in
accordance with the terms of the Trust Indenture, as amended, governing Marine.
 
                             PRINCIPAL UNITHOLDERS
 
     The following table sets forth the persons known to Marine who own
beneficially more than five percent of the outstanding units of beneficial
interest as of June 30, 1998:
 
<TABLE>
<CAPTION>
                                          AMOUNT AND NATURE OF   PERCENT
  TITLE OF CLASS      NAME AND ADDRESS    BENEFICIAL OWNERSHIP   OF CLASS
  --------------      ----------------    --------------------   --------
<S>                  <C>                  <C>                    <C>
Units of Beneficial  L. C. Paslay          286,469 units,          14.32%
  Interest           1020 S. Ocean Blvd.   owned
                     Manalapan, FL 33462   of record
                                           and beneficially*
</TABLE>
 
---------------
 
* Does not include 27,225 units held in trust in the name of L. C. Paslay, as
  Co-Trustee with NationsBank of Texas, N.A., for the benefit of Patricia L.
  Martin, daughter of Mr. Paslay.
 
     There are no executive officers or directors of Marine. NationsBank of
Texas, N.A. does not beneficially own any units of beneficial interest.
 
                                 MISCELLANEOUS
 
        EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K
 
     (a) Financial Statements -- see "Financial Statements and Supplementary
Data" above.
 
     The consolidated financial statements, together with the related notes and
the report of KPMG Peat Marwick LLP, independent certified public accountants,
as contained in the Form 10-K of Tidelands Royalty Trust "B" for its fiscal year
ended December 31, 1997 and filed with the Securities and Exchange Commission,
are hereby incorporated herein by reference for all purposes.
 
     (b) Reports on Form 8-K -- No reports on Form 8-K have been filed during
the last quarter of the fiscal year ended June 30, 1998.
 
     (c) Exhibits:
 
<TABLE>
<S>                   <C>
          (3)         -- Indenture, as amended, of Marine, filed as Exhibit 3 to the Annual Report on Form
                         10-K of Marine Petroleum Trust for the fiscal year ended June 30, 1994, filed with
                         the Securities and Exchange Commission and incorporated by reference herein.
          (4)         -- Form of Certificate evidencing Unit(s) of Beneficial Interest, filed as Exhibit 4 to
                         the Annual Report on Form 10-K of Marine Petroleum Trust for the fiscal year ended
                         June 30, 1994, filed with the Securities and Exchange Commission and incorporated by
                         reference herein.
          (21)        -- Subsidiaries of Marine.
          (27)        -- Financial Data Schedule.
</TABLE>
 
                                       11
<PAGE>   14
 
                          INDEPENDENT AUDITORS' REPORT
 
The Trustee
Marine Petroleum Trust:
 
     We have audited the accompanying consolidated balance sheets of Marine
Petroleum Trust and subsidiary as of June 30, 1998 and 1997 and the related
consolidated statements of income and undistributed income and cash flows for
each of the years in the three-year period ended June 30, 1998. These financial
statements are the responsibility of the Trust's management. Our responsibility
is to express an opinion on these financial statements based on our audits.
 
     We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements. An audit also includes
assessing the accounting principles used and significant estimates made by
management, as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.
 
     In our opinion, the consolidated financial statements referred to above
present fairly, in all material respects, the financial position of Marine
Petroleum Trust and subsidiary as of June 30, 1998 and 1997 and the results of
their operations and their cash flows for each of the years in the three-year
period ended June 30, 1998, in conformity with generally accepted accounting
principles.
 
                                            KPMG PEAT MARWICK LLP
 
Dallas, Texas
August 12, 1998
 
                                       12
<PAGE>   15
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                          CONSOLIDATED BALANCE SHEETS
                             JUNE 30, 1998 AND 1997
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                 1998            1997
                                                              ----------      ----------
<S>                                                           <C>             <C>
Current assets:
  Cash and cash equivalents.................................  $1,922,336      $1,759,718
  Oil and gas royalties receivable..........................     399,007         835,230
  Receivables from affiliate (note 2).......................     116,377          64,580
                                                              ----------      ----------
          Total current assets..............................   2,437,720       2,659,528
                                                              ----------      ----------
Investment in affiliate (note 2)............................     306,670         285,478
Office equipment, at cost less accumulated depreciation
  of $21,351 in 1998 and $19,415 in 1997....................         555             272
Producing oil and gas properties............................           7               7
                                                              ----------      ----------
                                                              $2,744,952      $2,945,285
                                                              ==========      ==========
 
                              LIABILITIES AND TRUST EQUITY
 
Current liabilities:
  Accounts payable (note 3).................................  $  926,663      $  895,724
  Income taxes payable......................................       9,021           4,758
                                                              ----------      ----------
          Total liabilities.................................     935,684         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......................................   1,809,260       2,044,795
                                                              ----------      ----------
          Total trust equity................................   1,809,268       2,044,803
                                                              ----------      ----------
                                                              $2,744,952      $2,945,285
                                                              ==========      ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       13
<PAGE>   16
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
           CONSOLIDATED STATEMENTS OF INCOME AND UNDISTRIBUTED INCOME
                        THREE YEARS ENDED JUNE 30, 1998
 
<TABLE>
<CAPTION>
                                                            1998          1997          1996
                                                         ----------    ----------    ----------
<S>                                                      <C>           <C>           <C>
Income:
  Oil and gas royalties................................  $2,577,126    $3,645,004    $2,841,549
  Equity in earnings of affiliate (note 2).............     461,095       319,251       384,753
  Interest income......................................      99,915       100,705        92,275
                                                         ----------    ----------    ----------
                                                          3,138,136     4,064,960     3,318,577
                                                         ----------    ----------    ----------
Expenses:
  Taxes other than income..............................          63           282           276
  General and administrative...........................     146,303       142,781       120,549
                                                         ----------    ----------    ----------
                                                            146,366       143,063       120,825
                                                         ----------    ----------    ----------
          Income before federal income taxes...........   2,991,770     3,921,897     3,197,752
Federal income taxes of subsidiary.....................      11,312         7,700        11,900
                                                         ----------    ----------    ----------
          Net income...................................   2,980,458     3,914,197     3,185,852
Undistributed income at beginning of year..............   2,044,795     2,069,945     1,431,862
                                                         ----------    ----------    ----------
                                                          5,025,253     5,984,142     4,617,714
Distributions to unitholders...........................   3,215,993     3,939,347     2,547,769
                                                         ----------    ----------    ----------
Undistributed income at end of year....................  $1,809,260    $2,044,795    $2,069,945
                                                         ==========    ==========    ==========
Net income per unit....................................  $     1.49    $     1.96    $     1.59
                                                         ==========    ==========    ==========
Distributions per unit.................................  $     1.61    $     1.97    $     1.27
                                                         ==========    ==========    ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       14
<PAGE>   17
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                        THREE YEARS ENDED JUNE 30, 1998
 
<TABLE>
<CAPTION>
                                                         1998           1997           1996
                                                      -----------    -----------    -----------
<S>                                                   <C>            <C>            <C>
Cash flows from operating activities:
  Net income........................................  $ 2,980,458    $ 3,914,197    $ 3,185,852
  Adjustments to reconcile net income to net cash
     provided by operating activities:
     Depreciation...................................        1,936            699            701
     Equity in undistributed earnings of
       affiliate....................................      (21,192)       (18,996)       (67,256)
     Change in assets and liabilities:
       Oil and gas royalties receivable.............      436,223       (247,305)      (200,465)
       Receivables from affiliate...................      (51,797)        38,146        (13,955)
       Accounts payable.............................       30,939             --             --
       Employment tax payable.......................           --         (2,459)        (1,377)
       Income taxes payable.........................        4,263         (5,912)         3,652
                                                      -----------    -----------    -----------
            Net cash provided by operating
               activities...........................    3,380,830      3,678,370      2,907,152
 
Cash flows used in investing activities -- purchase
  of office equipment...............................       (2,219)            --             --
 
Cash flows used in financing
  activities -- distributions to unitholders........   (3,215,993)    (3,939,347)    (2,547,769)
                                                      -----------    -----------    -----------
 
Net increase (decrease) in cash and cash
  equivalents.......................................      162,618       (260,977)       359,383
Cash and cash equivalents at beginning of year......    1,759,718      2,020,695      1,661,312
                                                      -----------    -----------    -----------
 
Cash and cash equivalents at end of year............  $ 1,922,336    $ 1,759,718    $ 2,020,695
                                                      ===========    ===========    ===========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       15
<PAGE>   18
 
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                        THREE YEARS ENDED JUNE 30, 1998
 
(1) SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES
 
  (a) General
 
     The Marine Petroleum Trust ("Trust") was established on June 1, 1956 with
the transfer of property to the Trust consisting of certain contract rights,
units of beneficial interest and common stock in exchange for units of
beneficial interest in the Trust. The contract rights entitled the Trust to
receive a .0075 overriding royalty interest in oil, gas and other mineral
leasehold interests acquired by Gulf Oil Corporation, now Chevron U.S.A., Inc.
("Chevron"), a subsidiary of Chevron Corporation, in certain areas of the Gulf
of Mexico prior to January 1, 1980. Substantially all royalty revenue is
received from Chevron.
 
     The Trust must distribute all income, after paying its liabilities and
obligations, to the unitholders during the months of March, June, September and
December each year. It cannot invest any of its money for any purpose and cannot
engage in a trade or business.
 
     A Louisiana trust can only exist for a short period of time; therefore, the
unitholders assigned their contract rights off-shore of Louisiana to Marine
Petroleum Corporation reserving a 98% net profits interest to themselves. The
net profits interest contract was transferred to the Trust along with the other
properties. The Trust is authorized to pay expenses of the Corporation should it
be necessary.
 
     The Trust is to continue until June 1, 2001, or until such later date as
holders of the units owning a majority of the outstanding units may designate,
but in any event, not more than 20 years from such designation. Alternatively,
instead of so extending the term of the Trust, the holders of the units owning a
majority of the outstanding units may direct the Trustee to create one or more
corporations to receive and hold the trust estate, or any portion thereof,
unless the Trustee shall have received written objection from any unitholder
within 20 days from the date of mailing to the unitholders of the first notice
of the proposed consent. However, the unitholders owning eighty percent (80%) of
the outstanding units may terminate the trust on any date.
 
  (b) Principles of Consolidation
 
     The consolidated financial statements include the Trust and its
wholly-owned subsidiary, Marine Petroleum Corporation. All material intercompany
accounts and transactions have been eliminated in consolidation.
 
  (c) Producing Oil and Gas Properties
 
     At the time the Trust was established, no determinable market value was
available for the assets transferred to the Trust; consequently, nominal values
were assigned. Accordingly, no allowance for depletion has been computed.
 
     All income from oil and gas royalties relate to proved developed oil and
gas reserves.
 
  (d) Undistributed Income
 
     The Trust indenture agreement provides that the corporate trustee is to
distribute all cash in the Trust, less an amount reserved for the payment of
accrued liabilities and estimated future expenses, to unitholders of record on
the 28th day of March, June, September and December of each year. If the 28th
falls on a Saturday, Sunday or legal holiday, the distribution is payable on the
immediately preceding business day. Undistributed income includes $743,519 and
$682,033 applicable to the subsidiary corporation at June 30, 1998 and 1997,
respectively.
 
                                       16
<PAGE>   19
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                        THREE YEARS ENDED JUNE 30, 1998
 
  (e) Federal Income Taxes
 
     No provision has been made for Federal income taxes on the Trust's income
since such taxes are the liability of the unitholders. Federal income taxes have
been provided on the income of the subsidiary corporation, excluding the 98% net
profits interest to be distributed to the Trust and deducting statutory
depletion.
 
  (f) Credit Risk Concentration and Cash Equivalents
 
     Financial instruments which potentially subject the Trust and its
wholly-owned subsidiary to concentrations of credit risk are primarily
investments in cash equivalents and receivables. The Trust and its wholly-owned
subsidiary place their cash investments with financial institutions or companies
that management considers credit worthy and limit the amount of credit exposure
from any one financial institution or company. The Trust has not experienced
significant problems collecting its receivables in the past.
 
     The Trust and its wholly-owned subsidiary had cash equivalents of
$1,885,861 and $1,726,851 at June 30, 1998 and 1997, respectively, which
consisted of money market accounts and money market mutual funds. For purposes
of the statements of cash flows, the Trust considers all investments with
initial maturities of three months or less to be cash equivalents.
 
  (g) Statements of Cash Flows
 
     The Trust's wholly-owned subsidiary made Federal income tax payments of
$7,049, $13,792, and $8,248 during the years ended June 30, 1998, 1997 and 1996,
respectively.
 
  (h) Fair Value of Financial Instruments
 
     The Trust and its wholly owned subsidiary define the fair value of a
financial instrument as the amount at which the instrument could be exchanged in
a current transaction between willing parties. The carrying value of cash and
cash equivalents, oil and gas royalties receivable, receivables from affiliates,
accounts payable, and taxes payable approximate fair value because of the short
maturities of those instruments.
 
  (i) Use of Estimates
 
     Management of the Trust and its wholly-owned subsidiary has made a number
of estimates and assumptions relating to the reporting of assets and liabilities
and the disclosure of contingent assets and liabilities to prepare these
financial statements in conformity with generally accepted accounting
principles. Actual results could differ from those estimates.
 
  (j) Income Per Unit
 
     The Trust adopted the provisions of SFAS No. 128, "Earnings per Share"
during 1998. Adoption of this standard did not have a material effect on the
calculation of income per unit. Income per unit is calculated by dividing net
income by the weighted average number of units of beneficial interest
outstanding during the period.
 
  (k) Significant Royalty Sources
 
     Royalty revenue received by Marine from Chevron and from Pennzoil
Exploration and Production Company ("Pennzoil") accounted in the aggregate for
approximately 85%, 81% and 88% of Marine's royalty revenue for the years ended
June 30, 1998, 1997 and 1996, respectively.
 
                                       17
<PAGE>   20
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                        THREE YEARS ENDED JUNE 30, 1998
 
(2) INVESTMENT IN AND RECEIVABLES FROM AFFILIATE -- TIDELANDS ROYALTY TRUST "B"
 
     At June 30, 1998 and 1997, the Trust owned 32.63% of the outstanding units
of interest in Tidelands Royalty Trust "B" ("Tidelands"). The 452,366 units
owned by the Trust had a quoted market value of $2,827,288, and $2,657,650 at
June 30, 1998 and 1997, respectively.
 
     The Trust and Tidelands share certain common costs which are allocated
based on their respective net revenues.
 
     The investment in affiliate is accounted for by the equity method. The
following summarizes changes in this account for 1998 and 1997:
 
<TABLE>
<CAPTION>
                                                                1998         1997
                                                              ---------    ---------
<S>                                                           <C>          <C>
Balance at beginning of year................................  $ 285,478    $ 266,482
Equity in earnings of affiliate.............................    461,095      319,251
Distribution of earnings....................................   (439,903)    (300,255)
                                                              ---------    ---------
Balance at end of year......................................  $ 306,670    $ 285,478
                                                              =========    =========
</TABLE>
 
     At June 30, 1998 and 1997, receivables from affiliate includes $104,523 and
$57,321, respectively, of income distributable to the Trust as a Tidelands
unitholder.
 
     The following summary financial statements have been derived from the
unaudited consolidated financial statements of Tidelands.
 
                                 BALANCE SHEETS
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                      JUNE 30
                                                              ------------------------
                                                                 1998          1997
                                                              ----------    ----------
<S>                                                           <C>           <C>
Cash and cash equivalents...................................  $1,924,316    $1,716,781
Oil and gas royalties receivable............................     138,934       282,748
Other.......................................................       4,830         3,980
                                                              ----------    ----------
                                                              $2,068,080    $2,003,509
                                                              ==========    ==========
</TABLE>
 
                          LIABILITIES AND TRUST EQUITY
 
<TABLE>
<S>                                                           <C>           <C>
Liabilities (including $329,559 and $184,816 payable to
  unitholders
  in 1998 and 1997, respectively)...........................  $1,166,776    $1,167,149
Corpus......................................................           2             2
Undistributed income........................................     901,302       836,358
                                                              ----------    ----------
                                                              $2,068,080    $2,003,509
                                                              ==========    ==========
</TABLE>
 
                                       18
<PAGE>   21
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                        THREE YEARS ENDED JUNE 30, 1998
 
                              STATEMENTS OF INCOME
 
<TABLE>
<CAPTION>
                                                            YEAR ENDED JUNE 30
                                                  --------------------------------------
                                                     1998          1997          1996
                                                  ----------    ----------    ----------
<S>                                               <C>           <C>           <C>
Income..........................................  $1,537,607    $1,065,247    $1,273,021
Expenses........................................     108,331        70,531        76,262
                                                  ----------    ----------    ----------
     Income before Federal income taxes.........   1,429,276       994,716     1,196,759
Federal income taxes of Tidelands' subsidiary...      16,150        16,300        17,600
                                                  ----------    ----------    ----------
     Net income.................................  $1,413,126    $  978,416    $1,179,159
                                                  ==========    ==========    ==========
</TABLE>
 
     Tidelands is a registrant with the Securities and Exchange Commission and
has filed a Form 10-K as of December 31, 1997.
 
(3) OVERPAID ROYALTIES
 
     The Trust's subsidiary, Marine Petroleum Corporation, has provided an
account payable of $758,250 to cover possible refunds that may be required upon
redetermination of gas prices for royalty payments in prior periods. During the
most recent fiscal year, Marine Petroleum Corporation determined that $137,474
of the previously-established account payable for possible royalty overpayments
no longer was required. Accordingly, during the most recent fiscal year, Marine
Petroleum Corporation reduced accounts payable, and increased net income by such
amount.
 
     During the most recent fiscal year, Chevron requested repayment for certain
royalties that Chevron believes were incorrectly paid to Marine Petroleum
Corporation during 1995, 1996 and 1997. Marine Petroleum Corporation established
a reserve of $167,000 in the current period to cover this potential liability.
In August of 1998, Marine Petroleum Corporation repaid $157,000 to Chevron to
resolve this matter.
 
(4) SUMMARY OF QUARTERLY FINANCIAL DATA (UNAUDITED)
 
     The following quarterly financial information for fiscal year 1998 and 1997
is unaudited; however, in the opinion of management, all adjustments necessary
to a fair statement of the results of operations for the interim periods have
been included.
 
<TABLE>
<CAPTION>
                                                                                     NET
                                             OIL AND GAS                            INCOME
                                              ROYALTIES    EXPENSES   NET INCOME   PER UNIT
                                             -----------   --------   ----------   --------
<S>                                          <C>           <C>        <C>          <C>
Quarter ended:
  September 30, 1997.......................  $  608,210     35,705      712,345       .36
  December 31, 1997........................     825,162     37,135      940,619       .47
  March 31, 1998...........................     562,845     38,230      685,609       .34
  June 30, 1998............................     580,909     35,296      641,885       .32
                                             ----------    -------    ---------      ----
                                             $2,577,126    146,366    2,980,458      1.49
                                             ==========    =======    =========      ====
Quarter ended:
  September 30, 1996.......................  $  861,011     27,858      927,649       .46
  December 31, 1996........................   1,085,760     47,881    1,137,457       .57
  March 31, 1997...........................     882,772     36,520      954,040       .48
  June 30, 1997............................     815,461     30,804      895,051       .45
                                             ----------    -------    ---------      ----
                                             $3,645,004    143,063    3,914,197      1.96
                                             ==========    =======    =========      ====
</TABLE>
 
                                       19
<PAGE>   22
                     MARINE PETROLEUM TRUST AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                        THREE YEARS ENDED JUNE 30, 1998
 
(5) SUPPLEMENTAL INFORMATION RELATING TO OIL AND GAS RESERVES (UNAUDITED)
 
     Oil and gas reserve information relating to the Trust's and Tidelands'
royalty interests is not presented because such information is not available to
the Trust or Tidelands. The Trust's share of oil and gas produced for its
royalty interests and the Trust's equity in oil and gas produced for Tidelands'
royalty interests were as follows:
 
<TABLE>
<CAPTION>
                                                            1998      1997      1996
                                                           -------   -------   -------
<S>                                                        <C>       <C>       <C>
Trust:
  Oil (barrels)..........................................   59,343    71,776    76,689
                                                           =======   =======   =======
  Gas (mcf)..............................................  582,594   879,452   700,209
                                                           =======   =======   =======
Tidelands:
  Oil (barrels)..........................................    3,245     2,780     2,847
                                                           =======   =======   =======
  Gas (mcf)..............................................  171,549   118,002   175,846
                                                           =======   =======   =======
</TABLE>
 
                                       20
<PAGE>   23
 
                                   SIGNATURES
 
     Pursuant to the requirements of Section 13 or 15(d) 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
                                              (Registrant)
 
                                            By: NATIONSBANK OF TEXAS, N.A.
                                              in its capacity as trustee of
                                              Marine Petroleum Trust and not in
                                              its individual capacity or
                                              otherwise
 
                                            By:      /s/ JANE J. SHEA
                                              ----------------------------------
                                                         Jane J. Shea
                                                        Vice President
 
Date: September 21, 1998
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, this
report has been signed below by the following persons on behalf of the
registrant and in the capacities and on the dates indicated.
 
                                            NATIONSBANK OF TEXAS, N.A.
                                              in its capacity as trustee of
                                              Marine Petroleum Trust and not in
                                              its individual capacity or
                                              otherwise
 
                                            By:      /s/ JANE J. SHEA
                                              ----------------------------------
                                                         Jane J. Shea
                                                        Vice President
 
Date: September 21, 1998
 
                                                     /s/ R. RAY BELL
                                            ------------------------------------
                                                        R. Ray Bell
                                             (Acting Chief Accounting Officer)
 
Date: September 21, 1998
 
                                       21
<PAGE>   24
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
      EXHIBITS                                              DESCRIPTION
      --------                                              -----------
<S>                   <C>
          (3)         -- Indenture, as amended, of Marine, filed as Exhibit 3 to the Annual Report on Form
                         10-K of Marine Petroleum Trust for the fiscal year ended June 30, 1994, filed with
                         the Securities and Exchange Commission and incorporated by reference herein.
          (4)         -- Form of Certificate evidencing Unit(s) of Beneficial Interest, filed as Exhibit 4 to
                         the Annual Report on Form 10-K of Marine Petroleum Trust for the fiscal year ended
                         June 30, 1994, filed with the Securities and Exchange Commission and incorporated by
                         reference herein.
          (21)        -- Subsidiaries of Marine.
          (27)        -- Financial Data Schedule.
</TABLE>