===============================================================================
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549

                                  FORM 10-Q
 
[X]   QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
      SECURITIES EXCHANGE ACT OF 1934 FOR THE QUARTERLY PERIOD
      ENDED SEPTEMBER 30, 1995
 
[ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
      SECURITIES EXCHANGE ACT OF 1934 FOR THE TRANSITION PERIOD
      FROM __________ TO __________
 
                          COMMISSION FILE NO. 1-8432
 
                             MESA OFFSHORE TRUST
            (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
            TEXAS                                              76-6004065
(STATE OR OTHER JURISDICTION OF                            (I.R.S. EMPLOYER
INCORPORATION OR ORGANIZATION)                            IDENTIFICATION NO.)
 
            TEXAS COMMERCE BANK
            NATIONAL ASSOCIATION
         CORPORATE TRUST DIVISION
             712 MAIN STREET
              HOUSTON, TEXAS                                    77002
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                      (ZIP CODE)
 
                                (713) 216-5100
             (REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE)
 
     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 the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date.
 
     As of November 10, 1995 -- 71,980,216 Units of Beneficial Interest in
Mesa Offshore Trust.
 
===============================================================================
<PAGE>
                       PART I -- FINANCIAL INFORMATION
 
ITEM 1.  FINANCIAL STATEMENTS
 
                             MESA OFFSHORE TRUST
 
                      STATEMENTS OF DISTRIBUTABLE INCOME
                                 (UNAUDITED)
<TABLE>
<CAPTION>
                                            THREE MONTHS ENDED            NINE MONTHS ENDED
                                              SEPTEMBER 30,                 SEPTEMBER 30,
                                       ----------------------------  ----------------------------
                                           1995           1994           1995           1994
                                       -------------  -------------  -------------  -------------
<S>                                    <C>            <C>            <C>            <C>          
Royalty income.......................  $     879,243  $   2,170,576  $   3,019,100  $   7,841,314
Interest income......................         23,686         29,842         70,513         78,551
General and administrative expense...        (70,502)       (66,531)      (322,042)      (333,235)
                                       -------------  -------------  -------------  -------------
     Distributable income............  $     832,427  $   2,133,887  $   2,767,571  $   7,586,630
                                       =============  =============  =============  =============
     Distributable income per unit...  $       .0116  $       .0296  $       .0385  $       .1053
                                       =============  =============  =============  =============
</TABLE>
              STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS

                                        SEPTEMBER 30,      DECEMBER 31,
                                            1995               1994
                                        -------------      -------------
                                         (UNAUDITED)
               ASSETS
Cash and short-term investments......   $   2,808,741      $   3,171,260
Interest receivable..................          23,686             25,821
Net overriding royalty interest in
  oil and gas properties.............     380,905,000        380,905,000
Accumulated amortization.............    (379,878,806)      (379,377,203)
                                        -------------      -------------
                                        $   3,858,621      $   4,724,878
                                        =============      =============
    LIABILITIES AND TRUST CORPUS
Reserve for Trust expenses...........   $   2,000,000      $   2,000,000
Distributions payable................         832,427          1,197,081
Trust corpus (71,980,216 units of
  beneficial interest
  authorized and outstanding)........       1,026,194          1,527,797
                                        -------------      -------------
                                        $   3,858,621      $   4,724,878
                                        =============      =============
 
 (The accompanying notes are an integral part of these financial statements.)
 
                                      1
<PAGE>
                               MESA OFFSHORE TRUST
 
                    STATEMENTS OF CHANGES IN TRUST CORPUS
                                 (UNAUDITED)
<TABLE>
<CAPTION>
                                             THREE MONTHS ENDED              NINE MONTHS ENDED
                                               SEPTEMBER 30,                   SEPTEMBER 30,
                                       ------------------------------  ------------------------------
                                            1995            1994            1995            1994
                                       --------------  --------------  --------------  --------------
<S>                                    <C>             <C>             <C>             <C>           
Trust corpus, beginning of period....  $    1,172,274  $    2,129,599  $    1,527,797  $    3,208,542
Distributable income.................         832,427       2,133,887       2,767,571       7,586,630
Distributions to unitholders.........        (832,427)     (2,133,887)     (2,767,571)     (7,586,630)
Amortization of net overriding
  royalty interest...................        (146,080)       (418,804)       (501,603)     (1,497,747)
                                       --------------  --------------  --------------  --------------
Trust corpus, end of period..........  $    1,026,194  $    1,710,795  $    1,026,194  $    1,710,795
                                       ==============  ==============  ==============  ==============
</TABLE>
 (The accompanying notes are an integral part of these financial statements.)

                                      2
 
                             MESA OFFSHORE TRUST
                        NOTES TO FINANCIAL STATEMENTS
                                 (UNAUDITED)
 
NOTE 1 -- TRUST ORGANIZATION
 
     The Mesa Offshore Trust (Trust) was created effective December 1, 1982
when Mesa Petroleum Co., predecessor to Mesa Limited Partnership, which was
predecessor to MESA Inc., transferred a 99.99% interest in the Mesa Offshore
Royalty Partnership (Partnership) to the Trust. The Partnership was created to
receive and hold a 90% net overriding royalty interest (the Royalty) in ten
producing and nonproducing oil and gas properties located in federal waters
offshore Louisiana and Texas (the Royalty Properties). MESA Inc. owns and
operates its assets through Mesa Operating Co., the operator of the Royalty
Properties. Mesa Operating Co. is also the managing general partner of the
Partnership (the Managing General Partner). As used in this report, the term
Mesa generally refers to the operator of the Royalty Properties, unless
otherwise indicated.
 
NOTE 2 -- BASIS OF PRESENTATION
 
     The accompanying unaudited financial information has been prepared by
Texas Commerce Bank National Association (Trustee) in accordance with the
instructions to Form 10-Q, and the Trustee believes such information includes
all the disclosures necessary to make the information presented not
misleading. The information furnished reflects all adjustments which are, in
the opinion of the Trustee, necessary for a fair presentation of the results
for the interim periods presented. The financial information should be read in
conjunction with the financial statements and notes thereto included in the
Trust's 1994 Annual Report on Form 10-K.

     The financial statements of the Trust are prepared on the following
basis:
 
          (a)  Royalty income recorded for a month is the Trust's interest in
     the amount computed and paid by Mesa to the Partnership for such month
     rather than either the value of a portion of the oil and gas produced by
     Mesa for such month or the amount subsequently determined to be 90% of
     the net proceeds for such month;
 
          (b)  Interest income, interest receivable and distributions payable
     to unitholders include interest to be earned on short-term investments
     from the financial statement date through the next distribution date;
 
          (c)  Trust administration expenses are recorded in the month they
     accrue;
 
          (d)  Amortization of the net overriding royalty interest, which is
     calculated on the basis of current royalty income in relation to
     estimated future royalty income, is charged directly to trust corpus
     since such amount does not affect distributable income; and
 
          (e)  Distributions payable are determined on a monthly basis and are
     payable to unitholders of record as of the last business day of each
     month. However, cash distributions are made quarterly in January, April,
     July and October, and include interest earned from the monthly record
     dates to the date of distribution.

     This basis for reporting royalty income is considered to be the most
meaningful because distributions to the unitholders for a month are based on
net cash receipts for such month. However, it will differ from the basis used
for financial statements prepared in accordance with generally accepted
accounting principles in several respects. Under such principles, royalty
income for a month would be based on net proceeds from production for such
month without regard to when calculated
 
                                      3
 
                             MESA OFFSHORE TRUST
                 NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                 (UNAUDITED)
or received and interest income would be calculated only for the periods
covered by the financial statements and would exclude interest from the period
end to the date of distribution.

     The instruments conveying the Royalty provide that Mesa will calculate
and pay the Partnership each month an amount equal to 90% of the net proceeds
for the preceding month. Generally, net proceeds means the excess of the
amounts received by Mesa from sales of oil and gas from the Royalty Properties
plus other cash receipts over operating and capital costs incurred.
 
                                      4
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
        RESULTS OF OPERATIONS
 
FINANCIAL REVIEW
 
     Distributable income for the third quarter of 1995 was $832,427,
representing $.0116 per unit, as compared to $2,133,887, representing $.0296
per unit, in the third quarter of 1994. The per unit amounts were earned by
month as follows:
 
                                         1995       1994
                                       ---------  ---------
July.................................  $   .0055  $   .0113
August...............................      .0032      .0091
September............................      .0029      .0092
                                       ---------  ---------
                                       $   .0116  $   .0296
                                       =========  =========
 
     Royalty income decreased to $879,243 in the third quarter of 1995,
compared to Royalty income of $2,170,576 in the third quarter of 1994. The
decrease in Royalty income was primarily due to lower natural gas prices and
lower natural gas, crude oil, condensate and natural gas liquids production.
 
     Production volumes for natural gas decreased to 850,550 Mcf in the third
quarter of 1995 from 1,287,825 Mcf in the third quarter of 1994 primarily due
to natural production declines. The average price received for natural gas was
$1.59 per Mcf in the third quarter of 1995 compared to $1.98 per Mcf in the
third quarter of 1994.
 
     Crude oil, condensate and natural gas liquids production decreased to
22,627 barrels in the third quarter of 1995 from 35,717 barrels in the third
quarter of 1994 primarily due to natural production declines. The average
price received for crude oil, condensate and natural gas liquids was $15.69
per barrel in the third quarter of 1995 compared to $15.06 per barrel in the
third quarter of 1994.
 
     During the first nine months of 1995, distributable income decreased to
$2,767,571 or $.0385 per unit from $7,586,630, or $.1053 per unit for the same
period in 1994. Royalty income for the nine months ended September 30, 1995
decreased to $3,019,100 from $7,841,314 for the same period in 1994, primarily
due to lower production and natural gas prices.
 
     For the nine months ended September 30, 1995, natural gas production
decreased to 2,960,391 Mcf from 4,327,347 Mcf for the nine months ended
September 30, 1994. Crude oil, condensate and natural gas liquids production
decreased to 92,241 barrels in the first nine months of 1995 compared to
142,162 barrels in the same period of 1994. These production decreases were
primarily attributable to natural production declines.
 
OPERATIONAL REVIEW

     Mesa has advised the Trust that during the third quarter its offshore gas
production was marketed under short term contracts at spot market prices to
multiple purchasers, including Natural Gas Clearinghouse, Penn Union Energy and
Neste, and that it expects to continue to market its production under short term
contracts for the forseeable future. Mesa has also advised the Trust that it
will consider multi-month contracts for the winter heating season if favorable
price provisions can be secured. Spot market prices for natural gas in the third
quarter of 1995 were generally lower than spot market prices in the third
quarter of 1994.

     The amount of cash distributed by the Trust is dependent on, among other
things, the sales prices and quantities of gas, crude oil, condensate and
natural gas liquids produced from the Royalty Properties. Substantial
uncertainties exist with regard to future gas and oil prices, which are
subject to

                                      5
 
fluctuations due to the regional supply and demand for natural gas and oil,
production levels and other activities of OPEC and other oil and gas
producers, weather, industrial growth, conservation measures, competition and
other variables.

     Brazos A-7 and A-39 natural gas production decreased in the third quarter
of 1995 as compared to the third quarter of 1994 primarily due to natural
production decline. Mesa has advised the Trust that it purchased a three
dimensional seismic survey of the A-7 block at a cost of $222,000 ($200,000 net
to the Trust). Mesa is currently evaluating the survey.

     South Marsh Island 155 and 156 natural gas production decreased in the
third quarter of 1995 as compared to the third quarter of 1994 primarily due to
the continued decline in production from the A-19 well. The A-19 well is
currently producing 3.0 MMcf of gas per day and 260 Bbls of condensate per day
compared to 4.8 MMcf of gas per day and 365 BBls of condensate per day at the
same time in 1994. During 1994 Mesa obtained a new seismic survey for block 155
to better evaluate exploration and development opportunities. The cost of the
survey was approximately $280,000 ($176,000 net to the Trust). In the first
quarter of 1995, Mesa's management approved the purchase of additional
three-dimensional seismic data for the west half of block 156 at an estimated
cost of $198,000 ($125,000 net to the Trust). Mesa has advised the Trust that it
now plans to drill up to five development and exploratory wells from existing
platforms on the South Marsh Island 155 and 156 blocks. Drilling is expected to
commence in the fourth quarter of 1995, pending rig availability, and is
expected to continue for approximately six months. The cost of this drilling is
estimated at $22 million ($14 million net to the Trust). The number of wells
drilled and the eventual cost of the program will depend on drilling success as
the program progresses. Distributions to the Trust are expected to stop in
November 1995 and will not resume until Mesa recovers the Trust's share of
drilling costs. See "Termination of the Trust" below.

     West Delta 61 and 62 natural gas production decreased in the third quarter
of 1995 as compared to the third quarter of 1994 primarily due to natural
production decline. The Trust is receiving royalty income from this property
pursuant to a farmout agreement with another operator. The interest in the
farmout wells which is attributable to the Trust consists of a 7.5% net profits
interest. In addition, Mesa has advised the Trust that it has purchased a three
dimensional seismic survey of this property at a cost of approximately $513,000
($462,000 net to the Trust). The data from this survey is currently being
evaluated by Mesa.

     Matagorda Island 624 natural gas production decreased in the third quarter
of 1995 as compared to the third quarter of 1994 primarily due to overall
natural production declines on the property and gas balancing. The A-1 well is
currently producing approximately 2.4 MMcf of gas per day and 48 barrels of
condensate per day compared to 2.3 MMcf of natural gas and 44 barrels of
condensate at the same time last year. Mesa successfully drilled the A-8
development well in the fourth quarter of 1995 to a total depth of 9,470 feet at
an estimated cost of $3,272,000 ($957,000 net to the Trust). The well
encountered 29 feet of net gas pay and tested approximately 20 MMcf of natural
gas and 270 barrels of condensate per day.

TERMINATION OF THE TRUST

     The terms of the Mesa Offshore Trust Indenture provide that the Trust will
terminate upon the first to occur of the following events: (1) the total amount
of cash received per year by the Trust for each of three successive years
commencing after December 31, 1987 is less than 10 times one-third of the total
amount payable to the Trustee as compensation for such three year period or (2)
a vote by the unitholders in favor of termination. Because the Trust will
terminate in the event the total amount of cash received per year by the Trust
falls below certain levels, it would be possible for the Trust to terminate even
though some of the Royalty Properties continued to have remaining productive
lives. In addition, information provided by Mesa indicates that approximately
80% of the future net revenues of the Trust are expected to be received by the
Trust over the next three years. For information regarding the estimated
remaining life of each of the Royalty Properties and the

                                      6

estimated future net revenues of the Trust based on information provided by
Mesa, see the Trust's 1994 Annual Report on Form 10-K. Upon termination of the
Trust, the Trustee will sell for cash all the assets held in the Trust estate
and make a final distribution to unitholders of any funds remaining after all
Trust liabilities have been satisfied. The discussion set forth above is
qualified in its entirety by reference to the Trust Indenture itself, which is
available upon request from the Trustee.

     Amounts paid to the Trustee as compensation were $177,500, $207,000 and
$227,000 for the years 1994, 1993 and 1992, respectively. Royalty income of
$9,104,615 for 1994 was above the termination threshold prescribed in the
Indenture.

     The terms of the First Amended and Restated Articles of General
Partnership of the Partnership provide that the Partnership shall dissolve
upon the occurrence of any of the following: (a) December 31, 2030; (b) the
election of the Trustee to dissolve the Partnership; (c) the termination of
the Trust; (d) the bankruptcy of the Managing General Partner; or (e) the
dissolution of the Managing General Partner or its election to dissolve the
Partnership; provided that the Managing General Partner shall not elect to
dissolve the Partnership so long as the Trustee remains the only other partner
of the Partnership. In the event of a dissolution of the Partnership and a
subsequent winding up and termination thereof, the assets of the Partnership
(i.e., the Royalty interest) could either (i) be distributed in kind ratably
to the Managing General Partner and the Trustee or (ii) be sold and the
proceeds thereof distributed ratably to the Managing General Partner and the
Trustee. In the event of a sale of the Royalty and a distribution of the cash
proceeds to the Trustee, the Trustee would make a final distribution to
unitholders of such cash proceeds plus any other cash held by the Trust after
the payment of or provision for all liabilities of the Trust, and the Trust
would be terminated. The discussion set forth above is qualified in its
entirety by reference to the Partnership Agreement itself, which is available
upon request from the Trustee.

     MESA Inc. has advised the Trust that it is highly leveraged with over $1.2
billion of long-term debt. MESA Inc.'s current financial forecasts indicate
that it will be unable to fund its principal and interest obligations in 1996
with cash flows from operating activities and available cash and securities
balances. MESA Inc. has been advised by its independent public accountants
that, if this matter is not resolved prior to the completion of their audit of
MESA Inc.'s financial statements for the year ended December 31, 1995, their
auditor's report on those financial statements will be modified to include a
discussion of the substantial doubt about Mesa's ability to continue as a
going concern. In the first quarter of 1995 MESA Inc. began an auction process
to sell all or a portion of its interests in the Hugoton field, which
interests represent two-thirds of MESA Inc.'s total equivalent oil and gas
reserves. None of the Trust's Royalty Properties are located in the Hugoton
field. The auction process was concluded in the second quarter of 1995 with no
acceptable bids received. On July 6, 1995, the MESA Inc. Board of Directors
approved a proposal to expand its review of strategic alternatives to include
consideration of the sale of MESA Inc. and a stock-for-stock merger. The MESA
Inc. Board also determined to continue to explore the sale of all or a portion
of the Hugoton field properties and to explore other restructuring
alternatives, including possible joint ventures involving the Hugoton
properties, asset sales, equity infusions, and refinancing transactions. The
MESA Inc. Board engaged independent financial advisors to manage these efforts
and to seek indications of interest from potential buyers of MESA Inc. or its
properties and of potential merger partners, both domestic and foreign. There
can be no assurance that a sale or merger of MESA Inc. or a sale of its
properties will be completed, or if completed, what the terms thereof will be.
MESA Inc.'s projected debt service problems, as well as any restructuring,
sale, merger or other strategic alternative, could have significant effects on
the Trust, although the precise nature of such effects cannot be predicted or
quantified at this time.

                                      7

     No assurance can be given by the Trust regarding MESA Inc.'s financial
condition. An event of bankruptcy of MESA Inc. that includes the Managing
General Partner would cause a dissolution of the Partnership which could cause
a termination of the Trust as described above. An event of bankruptcy of MESA
Inc. could also result in a delay in receipt of royalty payments by the Trust,
increased administrative expenses of the Trust and other effects which cannot
be predicted or quantified at this time.

     In addition, information provided by Mesa indicates that approximately
80% of the future net revenues of the Trust are expected to be received by the
Trust over the next three years. Therefore, unless additional drilling
activities are initiated and are successful, it is possible that as early as
1998 the Trust may commence a period of three successive years in which the
total amount of cash received per year by the Trust would be below the
termination threshold prescribed in the Indenture, resulting in termination of
the Trust.

     As discussed above, Mesa has completed drilling of the development well on
the Matagorda 624 property and has advised the Trust that it intends to drill up
to five developmental and exploratory wells from existing platforms on the South
Marsh Island 155 and 156 property beginning in November 1995. Mesa has advised
the Trust that it anticipates no royalty income will be paid to the Trust
beginning in November 1995 until Mesa recovers the drilling costs along with any
additional completion costs required if the drilling is successful. In addition,
if payments of royalty income to the Trust are resumed, distributions to
unitholders may be further delayed to allow the Trust to recover administrative
expenses paid during the period that royalty income was not paid to the Trust.
The recovery of costs associated with the Matagorda Island 624 and South Marsh
Island 155 and 156 drilling programs may cause the cash received by the Trust in
1996 to fall below the termination threshold prescribed in the Indenture, and
1996 could be the first of three successive years of below threshold income,
resulting in the termination of the Trust as early as the end of 1998. If the
drilling is successful, the effect on royalty income and Trust reserves will
depend on the quality and quantities of reserves found.

                                      8
<PAGE>
     The following tables provide a summary of the calculations of the net
proceeds attributable to the Partnership's royalty interest (unaudited):
<TABLE>
<CAPTION>
                                                      SOUTH
                                         BRAZOS       MARSH        HIGH       WEST      MATAGORDA
                                        A-7 AND     ISLAND 155    ISLAND    DELTA 61      ISLAND
                                          A-39       AND 156        567      AND 62        624          TOTAL
                                       ----------   ----------   ---------  ---------   ----------   -----------
<S>                                    <C>          <C>          <C>        <C>         <C>          <C>
THREE MONTHS ENDED
  SEPTEMBER 30, 1995:
    Ninety percent of gross
      proceeds.......................  $  391,710   $ 613,111    $  --      $ 595,298   $ 107,123    $ 1,707,242
    Less ninety percent of --
      Operating expenditures.........    (207,266)   (183,732 )     --       (189,743)   (119,612 )     (700,353)
    Capital costs recovered..........     (54,995)        (12 )     --         (4,924)     --            (59,931)
    Accrual for future abandonment
      costs..........................     (33,275)      1,139       --        (34,472)     (1,019 )      (67,627)
                                       ----------   ----------   ---------  ---------   ----------   -----------
    Net proceeds (excess costs)......  $   96,174   $ 430,506    $  --      $ 366,159   $ (13,508 )  $   879,331
                                       ==========   =========    =========  =========   =========    ===========
    Trust share of net proceeds
      (99.99%).......................                                                                $   879,243
                                                                                                     ===========
Production Volumes and Average
  Prices:
    Crude oil, condensate and natural
      gas liquids (Bbls).............         674      18,923       --          1,875       1,155         22,627
                                       ==========   =========    =========  =========   =========    ===========
    Average sales price per Bbl......  $    16.36   $   15.74    $  --      $   15.01   $   15.53    $     15.69
                                       ==========   =========    =========  =========   =========    ===========
    Natural gas (Mcf)................     241,700     207,324       --        342,932      58,594        850,550
                                       ==========   =========    =========  =========   =========    ===========
    Average sales price per Mcf......  $     1.58   $    1.52    $  --      $    1.65   $    1.52    $      1.59
                                       ==========   =========    =========  =========   =========    ===========
    Producing wells..................           3           2       --              2           2              9
</TABLE>
------------
 
o   The amounts shown are for Mesa Offshore Royalty Partnership.
 
o   The amounts for the three months ended September 30, 1995 represent actual
    production for the periods May 1995 through July 1995.
 
o   Capital costs recovered represent capital costs incurred during the
    current or prior periods to the extent that such costs have been recovered
    by Mesa from current period Gross Proceeds.
 
o   Producing wells indicates the number of wells capable of production as of
    the end of the period.
 
                                      9
<PAGE>
<TABLE>
<CAPTION>
                                                      SOUTH
                                        BRAZOS        MARSH         HIGH        WEST       MATAGORDA
                                          A-7       ISLAND 155     ISLAND     DELTA 61      ISLAND
                                       AND A-39      AND 156        567        AND 62         624         TOTAL
                                       ---------    ----------    --------   -----------   ---------   -----------
<S>                                    <C>          <C>           <C>        <C>           <C>         <C>        
THREE MONTHS ENDED
  SEPTEMBER 30, 1994:
    Ninety percent of gross
      proceeds.......................  $ 700,972    $ 940,922     $  --      $ 1,219,403   $226,195    $ 3,087,492
    Less ninety percent of --
      Operating expenditures.........   (212,107)    (232,132 )    (21,064)     (177,266)   (63,405 )     (705,974)
    Capital costs recovered..........     --          (17,347 )      --          --          (2,165 )      (19,512)
    Accrual for future abandonment
      costs..........................    (44,154)     (58,485 )      --          (42,366)   (46,208 )     (191,213)
                                       ---------    ----------    --------   -----------   ---------   -----------
    Net proceeds (excess costs)......  $ 444,711    $ 632,958     $(21,064)  $   999,771   $114,417    $ 2,170,793
                                       =========    =========     ========   ===========   ========    ===========
    Trust share of net proceeds
      (99.99%).......................                                                                  $ 2,170,576
                                                                                                       ===========
Production Volumes and Average
  Prices:
    Crude oil, condensate and natural
      gas liquids (Bls)..............     (1,367)      29,453        --            6,104      1,527         35,717
                                       =========    =========     ========   ===========   ========    ===========
    Average sales price per Bbl......  $   14.51    $   15.10     $  --      $     14.48   $  16.02    $     15.06
                                       =========    =========     ========   ===========   ========    ===========
    Natural gas (Mcf)................    364,932      244,799        --          570,959    107,135      1,287,825
                                       =========    =========     ========   ===========   ========    ===========
    Average sales price per Mcf......  $    1.98    $    2.03     $  --      $      1.98   $   1.88    $      1.98
                                       =========    =========     ========   ===========   ========    ===========
    Producing wells..................          3            2        --                2          3             10
</TABLE>
------------

o   The amounts shown are for Mesa Offshore Royalty Partnership.

o   The amounts for the three months ended September 30, 1994 represent actual
    production for the periods May 1994 through July 1994.

o   Capital costs recovered represent capital costs incurred during the
    current or prior periods to the extent that such costs have been recovered
    by Mesa from current period Gross Proceeds.

o   Producing wells indicates the number of wells capable of production as of
    the end of the period.
<PAGE>
<TABLE>
<CAPTION>
                                                         SOUTH
                                         BRAZOS          MARSH         HIGH          WEST        MATAGORDA
                                           A-7        ISLAND 155      ISLAND       DELTA 61       ISLAND
                                        AND A-39        AND 156         567         AND 62          624          TOTAL
                                       -----------    -----------    ---------    -----------    ---------    -----------
<S>                                    <C>            <C>            <C>          <C>            <C>          <C>
NINE MONTHS ENDED
  SEPTEMBER 30, 1995:
    Ninety percent of gross
      proceeds.......................  $ 1,355,242    $ 2,262,575    $  --        $ 2,007,236    $341,591     $ 5,966,644
    Less ninety percent of --
      Operating expenditures.........     (526,022)      (831,348)      --           (582,103)   (301,321 )    (2,240,794)
    Capital costs recovered..........     (209,034)      (166,104)      --            (62,267)      --           (437,405)
    Accrual for future abandonment
      costs..........................     (102,120)       (41,510)      --           (103,377)    (22,036 )      (269,043)
                                       -----------    -----------    ---------    -----------    ---------    -----------
    Net proceeds (excess costs)......  $   518,066    $ 1,223,613    $  --        $ 1,259,489    $ 18,234     $ 3,019,402
                                       ===========    ===========    =========    ===========    ========     ===========
    Trust share of net proceeds
      (99.99%).......................                                                                         $ 3,019,100
                                                                                                              ===========
Production Volumes and Average
  Prices:
    Crude oil, condensate and natural
      gas liquids (Bbls).............        2,489         77,801       --              8,519       3,432          92,241
                                       ===========    ===========    =========    ===========    ========     ===========
    Average sales price per Bbl......  $     16.17    $     14.78    $  --        $     14.86    $  15.56     $     14.85
                                       ===========    ===========    =========    ===========    ========     ===========
    Natural gas (Mcf)................      847,830        759,897       --          1,158,297     194,367       2,960,391
                                       ===========    ===========    =========    ===========    ========     ===========
    Average sales price per Mcf......  $      1.55    $      1.46    $  --        $      1.62    $   1.48     $      1.55
                                       ===========    ===========    =========    ===========    ========     ===========
    Producing wells..................            3              2       --                  2           2               9
</TABLE>
------------

o   The amounts shown are for Mesa Offshore Royalty Partnership.
 
o   The amounts for the nine months ended September 30, 1995 represent actual
    production for the periods November 1994 through July 1995.

o   Capital costs recovered represent capital costs incurred during the
    current or prior periods to the extent that such costs have been recovered
    by Mesa from current period Gross Proceeds.
 
o   Producing wells indicates the number of wells capable of production at the
    end of the period.
 
                                      10
<PAGE>
<TABLE>
<CAPTION>
                                                        SOUTH
                                         BRAZOS         MARSH         HIGH         WEST
                                           A-7       ISLAND 155      ISLAND      DELTA 61     MATAGORDA
                                        AND A-39       AND 156         567        AND 62      ISLAND 624      TOTAL
                                       -----------   -----------   -----------  -----------   ----------   ------------
<S>                                    <C>           <C>           <C>          <C>           <C>          <C>         
NINE MONTHS ENDED
  SEPTEMBER 30, 1994:
    Ninety percent of gross
      proceeds.......................  $ 2,408,611   $ 3,659,982   $   --       $ 4,295,725   $ 753,153    $ 11,117,471
    Less ninety percent of --
      Operating expenditures.........     (531,494)     (809,600)      (21,468)    (607,416)   (243,399 )    (2,213,377)
    Capital costs recovered..........      --           (139,781)      --           --         (353,560 )      (493,341)
    Accrual for future abandonment
     costs...........................     (153,157)     (116,278)      --          (201,728)    (97,491 )      (568,654)
                                       -----------   -----------   -----------  -----------   ----------   ------------
    Net proceeds (excess costs)......  $ 1,723,960   $ 2,594,323   $   (21,468) $ 3,486,581   $  58,703    $  7,842,099
                                       ===========   ===========   ===========  ===========   =========    ============
    Trust share of net proceeds (99.99%)..                                                                 $  7,841,314
                                                                                                           ============
Production Volumes and Average
  Prices:
    Crude oil, condensate and natural
      gas liquids (Bbls).............        1,652       116,187       --            21,641       2,682         142,162
                                       ===========   ===========   ===========  ===========   =========    ============
    Average sales price per Bbl......  $     11.88   $     12.92   $   --       $     12.32   $   14.47    $      12.85
                                       ===========   ===========   ===========  ===========   =========    ============
    Natural gas (Mcf)................    1,118,623     1,046,930       --         1,846,720     315,074       4,327,347
                                       ===========   ===========   ===========  ===========   =========    ============
    Average sales price per Mcf......  $      2.14   $      2.06       --       $      2.18   $    2.27    $       2.15
                                       ===========   ===========   ===========  ===========   =========    ============
    Producing wells..................            3             2       --                 2           3              10
</TABLE>
------------
 
o   The amounts shown are for Mesa Offshore Royalty Partnership.
 
o   The amounts for the nine months ended September 30, 1994 represent actual
    production for the periods November 1993 through July 1994.
 
o   Capital costs recovered represent capital costs incurred during the
    current or prior periods to the extent that such costs have been recovered
    by Mesa from current period Gross Proceeds.
 
o   Producing wells indicates the number of wells capable of production as of
    the end of the period.
 
FEDERAL INCOME TAX MATTERS

     Information for computing the Federal income tax consequences of owning
Trust units during 1995 will be mailed to Unitholders during the first quarter
of 1996.
 
                                      11
<PAGE>
                                   PART II
 
ITEM 6.  EXHIBIT AND REPORTS ON FORM 8-K

     (A)  EXHIBITS
 
   (Asterisk indicates exhibit previously filed with the Securities and
   Exchange Commission and incorporated herein by reference.)
<TABLE>
<CAPTION>
                                                                                                 SEC FILE
                                                                                                    OR
                                                                                               REGISTRATION     EXHIBIT
                                                                                                  NUMBER         NUMBER
                                                                                               ------------     -------
       <S>         <C>                                                                            <C>             <C>
       4(a)        *Mesa Offshore Trust Indenture between Mesa Petroleum Co. and Texas
                    Commerce Bank National Association, as Trustee, dated December 15,
                    1982....................................................................      2-79673         10(gg)
       4(b)        *Overriding Royalty Conveyance between Mesa Petroleum Co. and Mesa
                    Offshore Royalty Partnership, dated December 15, 1982...................      2-79673         10(hh)
       4(c)        *Partnership Agreement between Mesa Offshore Management Co. and Texas
                    Commerce Bank National Association, as Trustee, dated December 15,
                    1982....................................................................      2-79673         10(ii)
       4(d)        *Amendment to Partnership Agreement between Mesa Offshore Management Co.,
                    Texas Commerce Bank National Association, as Trustee, and Mesa Operating
                    Limited Partnership, dated December 27, 1985 (Exhibit 4(d) to Form 10-K
                    for year ended December 31, 1992 of Mesa Offshore Trust)................       1-8432          4(d)
       4(e)        *Amendment to Partnership Agreement between Texas Commerce Bank National
                    Association, as Trustee and Mesa Operating dated as of January 5, 1994
                    (Exhibit 4(e) to Form 10-K for year ended December 31, 1993 of Mesa
                    Offshore Trust).........................................................       1-8432          4(e)
      27           Financial Data Schedule
</TABLE>
     (B)  REPORTS ON FORM 8-K

          None.

                                      12

                                  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.

                                          MESA OFFSHORE TRUST

                                                    TEXAS COMMERCE BANK
                                          By        NATIONAL ASSOCIATION
                                                         TRUSTEE

                                          By /s/     MICHAEL J. ULRICH
                                                     MICHAEL J. ULRICH
                                               SENIOR VICE PRESIDENT & TRUST
                                                        OFFICER
 Date:  November 13, 1995

     The Registrant, Mesa Offshore Trust, has no principal executive officer,
principal financial officer, board of directors or persons performing similar
functions. Accordingly, no additional signatures are available and none have
been provided.

                                      13