<PAGE>   1
 
================================================================================
                                   FORM 10-Q
 
                       SECURITIES AND EXCHANGE COMMISSION
 
                             Washington, D.C. 20549
 
(Mark One)
 
[X]          QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
                      SECURITIES AND EXCHANGE ACT OF 1934
 
For the quarterly period ended June 30, 1997.
 
                                       OR
 
[ ]          TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
                        SECURITIES EXCHANGE ACT OF 1934
 
For the transition period from .............. to ...............
 
Commission file number 1-8581
 
                   FREEPORT-McMoRan OIL AND GAS ROYALTY TRUST
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                                            <C>
                         TEXAS                                                72-6108468
     (State or other jurisdiction of incorporation                         (I.R.S. Employer
                    or organization)                                      Identification No.)
 
        TEXAS COMMERCE BANK NATIONAL ASSOCIATION                                 77002
                CORPORATE TRUST DIVISION                                      (Zip Code)
                    712 MAIN STREET
                     HOUSTON, TEXAS
        (Address of principal executive offices)
</TABLE>
 
       Registrant's telephone number, including area code: (713) 216-5447
 
                      ....................................
 
   (Former name, former address and former fiscal year, if changed since last
                                    report)
 
     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.
 
Yes  X   No  ______
    ___

================================================================================
<PAGE>   2
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                                                PAGE
                                                              --------
<S>                                                           <C>
Part I.  Financial Information
 
  Item 1.  Financial Statements:
     Statements of Royalty Proceeds and Distributable
      Cash..................................................    3
     Statements of Assets, Liabilities and Trust Corpus.....    3
     Statements of Changes in Trust Corpus..................    3
     Notes to Financial Statements..........................    4
     Report of Independent Public Accountants...............    7
 
  Item 2.  Management's Discussion and Analysis of Financial
     Condition and Results of Operations....................    8
 
Part II.  Other Information
 
  Item 6.  Exhibits and Reports on Form 8-K.................    12
 
Signature...................................................    13
</TABLE>
 
                                      --2--
<PAGE>   3
 
                         PART I.  FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS.
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
             STATEMENTS OF ROYALTY PROCEEDS AND DISTRIBUTABLE CASH
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                               THREE MONTHS ENDED            SIX MONTHS ENDED
                                                    JUNE 30,                     JUNE 30,
                                            -------------------------   --------------------------
                                               1997          1996          1997           1996
                                            -----------   -----------   -----------    -----------
<S>                                         <C>           <C>           <C>            <C>
Royalty proceeds..........................  $        --   $        --   $        --    $        --
Trust administrative expenses.............      (84,722)     (168,876)     (172,337)      (231,542)
Interest income...........................       19,416        21,040        38,227         40,376
Reserve for future Trust expenses.........       65,306       147,836       134,110        191,166
                                            -----------   -----------   -----------    -----------
Distributable cash........................  $        --   $        --   $        --    $        --
                                            ===========   ===========   ===========    ===========
Distributable cash per Unit...............  $        --   $        --   $        --    $        --
                                            ===========   ===========   ===========    ===========
Units outstanding.........................   14,975,390    14,975,390    14,975,390     14,975,390
                                            ===========   ===========   ===========    ===========
</TABLE>
 
               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
 
<TABLE>
<CAPTION>
                                                                JUNE 30,       DECEMBER 31,
                                                                  1997             1996
                           ASSETS                             -------------    -------------
                                                               (UNAUDITED)
<S>                                                           <C>              <C>
Cash and short-term investments.............................  $   1,849,461    $   1,983,571
Net overriding royalty interest in oil and gas properties...    189,875,741      189,875,741
Less, adjustment to recorded cost of net overriding royalty
  interest in oil and gas properties........................    (25,431,543)     (25,431,543)
Less, accumulated amortization of net overriding royalty
  interest..................................................   (164,260,985)    (164,260,985)
                                                              -------------    -------------
          Total assets......................................  $   2,032,674    $   2,166,784
                                                              =============    =============
                LIABILITIES AND TRUST CORPUS
Reserve for future Trust expenses...........................  $   1,849,461    $   1,983,571
Trust corpus (14,975,390 Units of Beneficial Interest
  authorized,
  issued and outstanding)...................................        183,213          183,213
                                                              -------------    -------------
          Total liabilities and trust corpus................  $   2,032,674    $   2,166,784
                                                              =============    =============
</TABLE>
 
                     STATEMENTS OF CHANGES IN TRUST CORPUS
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                 SIX MONTHS ENDED
                                                                     JUNE 30,
                                                              -----------------------
                                                                1997         1996
                                                              --------    -----------
<S>                                                           <C>         <C>
Trust corpus, beginning of year.............................  $183,213    $   183,213
Royalty proceeds and interest income, net of trust
  administrative expenses and reserve for future Trust
  expenses..................................................        --             --
Distributions payable to Unit holders.......................        --             --
Amortization of net overriding royalty interest.............        --             --
                                                              --------    -----------
Trust corpus, end of period.................................  $183,213    $   183,213
                                                              ========    ===========
</TABLE>
 
   The accompanying notes are an integral part of these financial statements.
 
                                      --3--
<PAGE>   4
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
 
                         NOTES TO FINANCIAL STATEMENTS
1. THE TRUST
 
     Freeport-McMoRan Oil and Gas Royalty Trust (the Trust) was created
effective September 30, 1983. On that date, Freeport-McMoRan Inc. (FTX)
transferred a net overriding royalty interest in certain offshore oil and gas
properties to a Partnership (the Partnership) equal to 90 percent of the Net
Proceeds (as defined in the Conveyance referred to below) from FTX's working
interests in such properties and conveyed a 99.9 percent general partnership
interest in the Partnership to the Trust. Such net overriding royalty interest
is referred to herein as the "Royalty." The Overriding Royalty Conveyance which
created the Royalty is referred to herein as the "Conveyance." The Trust is
passive, with Texas Commerce Bank National Association as Trustee. The Trustee
has only such powers as are necessary for the collection and distribution of
revenues attributable to the Royalty, the payment of Trust liabilities and the
protection of Trust assets.
 
     The Trust Indenture provides generally that the Trust shall terminate upon
the first to occur of (i) the sale of all the Trust's interest in the
Partnership, or the sale by the Partnership of all the assets of the Partnership
including the Royalty, or (ii) a decision to terminate the Trust by the
affirmative vote of Unit holders representing a majority of the Units. The
Trustee is required to sell the Trust's interest in the Partnership, or cause
the Partnership to sell the Royalty, if the Trust's cash receipts for each of
three successive years are less than $3 million, thereby terminating the Trust
pursuant to (i) above. Upon the termination of the Trust under (ii) above, the
Trustee will sell the Trust's interest in the Partnership (or will cause the
Partnership to sell all of the assets of the Partnership). The Trustee will as
promptly as possible distribute the proceeds of any such sales according to the
respective interests and rights of the Unit holders after discharging all of the
liabilities of the Trust and, if necessary, setting up reserves in such amounts
as the Trustee in its discretion deems appropriate for contingent liabilities.
 
     The Trust's cash receipts last reached $3 million during 1995 and there
were no cash receipts in 1996. Accordingly, the Trust would have to receive cash
of at least $3 million during 1997 or 1998 to avoid termination, as described
above. Significant development costs, primarily at West Cameron Block 498, have
resulted in no cash receipts during the first six months of 1997 and have
increased the Class A cost carry-forward at June 30, 1997 to $7.3 million. In
light of the existing Class A cost carry-forward, which must be recouped by the
Working Interest Owner before any distributions may be made to the Trust, and
the additional capital costs projected at West Cameron Block 498 and the timing
of production therefrom, no cash receipts by the Trust are anticipated during
the remainder of 1997.
 
     Therefore, the Trust will be terminated unless the Trust has cash receipts
of at least $3 million during 1998. It is not possible at this time to predict
the Trust's cash receipts during 1998. Whether, and to what extent, the Trust
will have cash receipts during 1998 will depend primarily on the timing and the
rate of production from West Cameron Block 498, the prices of oil and natural
gas, the amount of future exploration and development costs and other factors.
 
                                      --4--
<PAGE>   5
 
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
2. THE ROYALTY
 
     Freeport-McMoRan Oil & Gas Company, a division of FTX (the Working Interest
Owner), presently owns the oil and gas interests burdened by the Royalty. The
Conveyance provides that the owner of the interests burdened by the Royalty will
calculate and pay monthly to the Partnership an amount equal to 90 percent of
the net proceeds for the preceding month. Net proceeds generally consist of the
excess of gross revenues received from the Royalty Properties (Gross Proceeds),
on a cash basis, over operating costs, capital expenditures and other charges,
on an accrual basis (Net Proceeds).
 
     On July 28, 1997, FTX and IMC Global, Inc. (IGL) announced their agreement
to merge through an exchange of common shares, with IGL as the surviving entity.
The proposed merger is subject to negotiation of a definitive agreement and
appropriate approvals. The definitive merger agreement is expected to be
completed within approximately 30 days, with completion of the merger
transaction by the end of 1997.
 
3. DISTRIBUTIONS TO UNIT HOLDERS
 
     As a result of the capital costs incurred during the past two years, a
cumulative excess Class A cost carry-forward of $7,299,136 existed as of June
30, 1997. This carry-forward is subject to and includes interest due the Working
Interest Owner at the prime rate, which totaled $169,346 net to the Trust during
the six month period of 1997. This excess Class A cost carry-forward must be
recouped out of future Net Proceeds before distributions to the Unit holders can
be resumed.
 
4. GAS BALANCING ARRANGEMENTS
 
     As a result of past curtailments in gas takes by the principal purchaser of
production from the Royalty Properties, certain quantities of gas have been sold
by other parties with interests in the Royalty Properties pursuant to gas
balancing arrangements. Proceeds from gas produced from the Royalty Properties
but sold by other parties pursuant to such balancing arrangements
(underproduction) are not included in Gross Proceeds for purposes of calculating
the Royalty. In the future, the Working Interest Owner will be entitled to sell
volumes equal to such underproduction or receive cash settlements. On certain of
the Royalty Properties, a cash settlement may be required, depending on future
results, because of the lack of sufficient remaining reserves from which to
makeup any underproduction. As of June 30, 1997, the unrecovered quantity of gas
sold by third parties pursuant to such gas balancing arrangements since
inception of the Trust through March 31, 1997 was approximately 1.7 billion
cubic feet (bcf), net to the Trust. Gross Proceeds will be increased in future
periods when the Working Interest Owner is compensated either through the sale
of gas or through cash settlements, the amount and timing of which are
uncertain.
 
5. ESTABLISHMENT OF AN EXPENSE RESERVE
 
     Because of the decline in Royalty income, at certain times since late 1993
the Trust has been unable to pay its ongoing administrative expenses. To permit
the Trust to pay its routine administrative expenses during the time the Trust
incurs a Class A cost deficit, the Trustee, in accordance with the Trust
Indenture,
 
                                      --5--
<PAGE>   6
 
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
established an expense reserve of $2.4 million, of which $1,849,461 remained as
of June 30, 1997. Because of the cumulative excess Class A cost carry-forward
(Note 3), $134,110 was withdrawn from the expense reserve to pay Trust
administrative expenses during the first six months of 1997. There will be
income tax consequences to the Unit holders for such reserve as described in
Note 6 below.
 
     The funding for this reserve is deposited with Texas Commerce Bank and
invested in Texas Commerce Bank collateralized certificates of deposit. The
average interest rate earned on these funds for the second quarter of 1997 was
4.15 percent.
 
6. FEDERAL INCOME TAX MATTERS
 
     Unit holders are required to report taxable income for the Royalty income
received by the Trust and deposited to the expense reserve even if no
distributions were received by the Unit holders. The expense reserve established
for Trust administrative expenses described in Note 5 above will give rise to
future income tax deductions as additional administrative expenses are incurred
and paid with funds deposited in the reserve.
 
7. RESERVE FOR FUTURE ESTIMATED ABANDONMENT COSTS
 
     Estimated future abandonment costs, based on current laws and regulations,
are accrued over the life of the Trust's properties. As of June 30, 1997, the
estimated remaining aggregate abandonment costs to be incurred for all of the
Trust's properties totaled $11.4 million net to the Trust, of which $10.5
million has been withheld from distributions to Unit holders. Estimated future
abandonment costs are by their nature imprecise and can be expected to be
revised over time because of changes in general and specific cost levels,
government regulations, operations and technology. Any adjustments to estimated
abandonment costs or variances to actual costs will reduce or increase future
distributable cash accordingly.
 
                             ---------------------
 
     THE INFORMATION FURNISHED HEREIN SHOULD BE READ IN CONJUNCTION WITH THE
FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST FINANCIAL STATEMENTS FOR THE YEAR
ENDED DECEMBER 31, 1996, WHICH ARE CONTAINED IN ITS ANNUAL REPORT ON FORM 10-K
FOR 1996.
 
                                      --6--
<PAGE>   7
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
 
                    REPORT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
To Texas Commerce Bank National Association (Trustee)
and the Unit Holders of Freeport-McMoRan Oil and Gas Royalty Trust:
 
     We have reviewed the accompanying statement of assets, liabilities and
trust corpus of Freeport-McMoRan Oil and Gas Royalty Trust as of June 30, 1997,
and the related statements of royalty proceeds and distributable cash for the
three-month and six-month periods ended June 30, 1997 and 1996 and the
statements of changes in trust corpus for the six month periods ended June 30,
1997 and 1996. These financial statements are the responsibility of the Working
Interest Owner.
 
     We conducted our reviews in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical review
procedures to financial data and making inquiries of persons responsible for
financial and accounting matters. It is substantially less in scope than an
audit in accordance with generally accepted auditing standards, the objective of
which is the expression of an opinion regarding the financial statements taken
as a whole. Accordingly, we do not express such an opinion.
 
     These financial statements were prepared on the cash basis of accounting,
which is a comprehensive basis of accounting other than generally accepted
accounting principles.
 
     Based on our reviews, we are not aware of any material modifications that
should be made to the financial statements referred to above for them to be in
conformity with the cash basis of accounting.
 
     We have previously audited, in accordance with generally accepted auditing
standards, the statement of assets, liabilities and trust corpus of
Freeport-McMoRan Oil and Gas Royalty Trust as of December 31, 1996 and, in our
report dated March 7, 1997, we expressed an unqualified opinion on that
statement.
 
                                          ARTHUR ANDERSEN LLP
 
New Orleans, Louisiana,
August 1, 1997
 
                                      --7--
<PAGE>   8
 
ITEM 2.MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
       OF OPERATIONS.
 
     The information contained herein regarding operations and exploration and
development activities on the properties burdened by the Royalty has been
furnished by the Working Interest Owner who obtained this information from the
relevant operators. For convenience, references are made to the Notes to
Financial Statements.
 
     The following discussion includes forward-looking statements within the
meaning of Section 27A of the Securities Act of 1933 and Section 21E of the
Securities Exchange Act of 1934. Although it is believed that these
forward-looking statements are based on reasonable assumptions, important
factors could cause actual results to differ materially from those in the
forward-looking statements herein, including the timing and extent of changes in
commodity prices for oil and gas, environmental risks, drilling and operating
risks, risks related to exploration and development, uncertainties about the
Trust's reserves, government regulations and other matters beyond the control of
the Trustee and the Working Interest Owner.
 
OPERATIONAL ACTIVITIES
 
     At the West Cameron Block 498 field, four exploratory wells were drilled in
1994 and 1995, which discovered oil and natural gas reserves. Construction of
two platforms and production facilities began in January 1997. The first
platform was installed in the first quarter of 1997 from which the first
development well was drilled in the second quarter but did not encounter its
objectives and was temporarily abandoned. Following the first well, the second
and third development wells were successfully drilled and completion operations
commenced during August 1997. Installation of the second platform and production
facilities is scheduled for the end of the third quarter of 1997, with first
production expected in late October 1997. The operator currently plans to drill
additional development wells and is considering further exploration on this
block. The Working Interest Owner has a 23.1% working interest and 19.2% net
revenue interest in the field.
 
     Drilling operations were completed on an exploratory well on Breton Sound
Block 55 during the second quarter of 1996. This well initiated production in
July 1997. The well has recently tested at a rate of 5 million cubic feet of
natural gas and 132 barrels of condensate per day on 30/64th inch choke and
9,234 pounds per square inch. Production performance will determine if an offset
well will be drilled. There is an additional productive zone with an estimated
39 feet of net gas pay in the well which is behind pipe and has not been
flow-tested. The Working Interest Owner owns an 18.75% working interest in
Breton Sound Block 55 and a 9.375% working interest and a 6.25% revenue interest
in this well pursuant to a co-development agreement with the owner of the
adjacent block.
 
     At the West Cameron Block 65 field, the Working Interest Owner is
negotiating an agreement to assign its interests and abandonment obligations to
the operator. The assignment is expected to occur during the third quarter of
1997 and would result in a reduction of estimated future abandonment costs of
approximately $0.1 million, net to the Trust. The Working Interest Owner has a
4.2% working interest and a 3.5% net revenue interest in the field.
 
     At the West Cameron Block 215 field, the operator is currently reviewing
development and exploration activities which may result in future capital
expenditures. The Working Interest Owner has a 31.3% working interest and a
26.1% net revenue interest in the field.
 
                                      --8--
<PAGE>   9
 
     At the West Delta Block 34 field, the last producing well was shut in
during July 1997. The operator is evaluating remedial work to determine whether
production can be re-established. The Working Interest Owner has a 30.0% working
interest and a 25.0% net revenue interest in the field.
 
CAPITAL RESOURCES AND LIQUIDITY
 
     The Trustee may sell or dispose of the Trust's interest in the Partnership,
or permit the Partnership to sell or dispose of all or any part of the Royalty
only as authorized by a vote of Unit holders, upon termination of the Trust and
in certain other limited circumstances. However, the Trust is directed to effect
such a sale (without any such vote) if the Trust's cash receipts for each of
three successive years are less than $3 million. The Trustee must distribute the
net proceeds of such sale (after satisfaction of any outstanding liabilities) to
the Unit holders.
 
     The Trust's cash receipts last reached $3 million during 1995 and there
were no cash receipts in 1996. Accordingly, the Trust would have to receive cash
of at least $3 million during 1997 or 1998 to avoid termination, as described
above. Significant development costs, primarily at West Cameron Block 498, have
resulted in no cash receipts during the first six months of 1997 and have
increased the Class A cost carry-forward at June 30, 1997 to $7.3 million. In
light of the existing Class A cost carry-forward, which must be recouped by the
Working Interest Owner before any distributions may be made to the Trust, and
the additional capital costs projected at West Cameron Block 498 and the timing
of production therefrom, no cash receipts by the Trust are anticipated during
the remainder of 1997.
 
     Therefore, the Trust will be terminated unless the Trust has cash receipts
of at least $3 million during 1998. It is not possible at this time to predict
the Trust's cash receipts during 1998. Whether, and to what extent, the Trust
will have cash receipts during 1998 will depend primarily on the timing and the
rate of production from West Cameron Block 498, the prices of oil and natural
gas, the amount of future exploration and development costs and other factors.
 
     Total exploration and development costs for the remainder of 1997 are
presently estimated by the Working Interest Owner to be approximately $6.2
million net to the Trust, primarily for the development of West Cameron Block
498, based on cost estimates provided by the operators of the Royalty
Properties. Those estimates may vary from actual costs depending on the success
of drilling, particular circumstances encountered during drilling and many other
factors outside the control of the operators. Additional exploration may be
proposed by the operators of certain Royalty Properties. After analyzing each
proposal, the Working Interest Owner will determine whether or not to
participate in additional exploratory operations.
 
     Estimated future abandonment costs, based on current laws and regulations,
are accrued over the life of the Trust's properties (Note 7). As of June 30,
1997, the estimated remaining aggregate abandonment costs to be incurred for all
of the Trust's properties totaled $11.4 million net to the Trust, of which $10.5
million has been withheld from distributions to Unit holders. Based on these
amounts, future distributions to Unit holders would be reduced by approximately
$0.06 per Unit over the remaining productive lives of the properties, subject to
future revisions of such costs because of changes in general and specific cost
levels, government regulations, operations and technology.
 
                                      --9--
<PAGE>   10
 
     At certain times since late 1993, the Trust has been unable to pay its
ongoing administrative expenses. To permit the Trust to pay its administrative
expenses during the time the Trust incurs a Class A cost deficit, the Trustee,
in accordance with the Trust Indenture, established a $2.4 million Trust
administrative expense reserve to pay such expenses (Note 5), of which $1.8
million remained at June 30, 1997.
 
RESULTS OF OPERATIONS
 
     There were no cash distributions to the Unit holders during the first six
months of 1997 or 1996, primarily because of significant capital expenditures.
During the second quarter of 1997, Total Costs exceeded Gross Proceeds by
approximately $3.9 million, because of the capital costs incurred to develop
Breton Sound Block 55 and West Cameron Block 498. As a result, the Class A cost
carry-forward increased to $7.3 million net to the Trust as of June 30, 1997
(Note 3). Because of the Class A cost carry-forward, the Trust administrative
expenses were paid from the expense reserve during 1997. The calculation of
distributable cash for each period follows:
 
<TABLE>
<CAPTION>
                                            THREE MONTHS ENDED             SIX MONTHS ENDED
                                                 JUNE 30,                      JUNE 30,
                                         -------------------------    --------------------------
                                            1997           1996          1997           1996
                                         -----------    ----------    -----------    -----------
<S>                                      <C>            <C>           <C>            <C>
Gross Proceeds(1)......................  $   799,415    $1,090,451    $ 1,614,627    $ 1,932,045
Total Costs(2).........................   (4,746,328)     (904,219)    (6,968,118)    (3,076,081)
Excess Class A cost (recovery) carry-
  forward, net(3)......................    3,946,913      (186,232)     5,353,491      1,144,036
                                         -----------    ----------    -----------    -----------
Net Proceeds...........................           --            --             --             --
Percentage attributable to Royalty.....         90.0%         90.0%          90.0%          90.0%
                                         -----------    ----------    -----------    -----------
Amounts payable attributable to
  Royalty..............................           --            --             --             --
Percentage attributable to the Trust...         99.9%         99.9%          99.9%          99.9%
                                         -----------    ----------    -----------    -----------
Royalty Proceeds.......................           --            --             --             --
Trust administrative expenses..........      (84,722)     (168,876)      (172,337)      (231,542)
                                         -----------    ----------    -----------    -----------
                                             (84,722)     (168,876)      (172,337)      (231,542)
Interest income........................       19,416        21,040         38,227         40,376
Reserve for future Trust expenses(4)...       65,306       147,836        134,110        191,166
                                         -----------    ----------    -----------    -----------
Distributable cash.....................  $        --    $       --    $        --    $        --
                                         ===========    ==========    ===========    ===========
</TABLE>
 
---------------
 
(1) Represents amounts received by the Working Interest Owner during the three
     and six month periods ended in May of such year.
 
(2) Represents amounts accrued by the Working Interest Owner during the three
     and six month periods ended in May of such year. Includes accrued interest
     of $110,873 and $169,346 for the three and six month periods of 1997,
     respectively.
 
(3) Recoveries represent Class A costs incurred in prior periods and recovered
     in current period; carry-forwards represent Class A costs incurred in the
     applicable periods that remained outstanding as of the end of such periods.
 
(4) Represents withdrawals from the Trust administrative expense reserve during
     the respective periods.
 
                                     --10--
<PAGE>   11
 
     Gross Proceeds, which includes gas and oil revenues, are calculated based
on amounts received by the Working Interest Owner. Operating information
follows:
 
<TABLE>
<CAPTION>
                                                  SECOND QUARTER              SIX MONTHS
                                               ---------------------     ---------------------
                                                 1997         1996         1997         1996
                                               --------     --------     --------     --------
<S>                                            <C>          <C>          <C>          <C>
Natural Gas
  Revenues (in millions).....................   $  0.4       $  0.7       $  0.8       $  1.3
  Sales volumes (in million cubic feet)......      161          246          298          537
  Average realization (per thousand cubic
     feet)...................................   $ 2.82       $ 2.91       $ 2.82       $ 2.45
Oil
  Revenues (in millions).....................   $  0.4       $  0.4       $  0.8       $  0.6
  Sales volumes (in thousands of barrels)....     16.3         20.4         34.5         35.4
  Average realization (per barrel)...........   $21.20       $18.36       $22.41       $17.36
</TABLE>
 
     Gas volumes for the 1997 periods decreased from 1996 levels because of the
substantial depletion of East Cameron Block 336 in mid-1996 and normal
production declines on the remaining producing properties. Oil volumes for the
1997 periods decreased because of normal production declines. Revenues for the
six-month period of 1997 benefited from an increase in average realizations
reflecting the rise in natural gas and oil market prices during that period.
 
     Costs consist of the following (in millions):
 
<TABLE>
<CAPTION>
                                                  SECOND QUARTER              SIX MONTHS
                                               ---------------------     ---------------------
                                                 1997         1996         1997         1996
                                               --------     --------     --------     --------
<S>                                            <C>          <C>          <C>          <C>
Lease operating expenses.....................   $  0.4       $  0.6       $  0.3       $  1.4
Exploration and development costs............      4.2          0.2          6.4          1.3
Abandonment costs withheld and other.........      0.1          0.1          0.2          0.4
                                                ------       ------       ------       ------
                                                $  4.7       $  0.9       $  6.9       $  3.1
                                                ======       ======       ======       ======
</TABLE>
 
     Lower lease operating expenses for the second-quarter and six-month periods
of 1997 resulted from several properties ceasing production and a downward
revision of accrued insurance costs. Second-quarter and six-month 1997
exploration and development costs relate to development at West Cameron Block
498 and Breton Sound Block 55. Exploration and development costs for the 1996
periods consisted primarily of exploration and development costs at Vermilion
Block 58 and West Cameron Block 498. Abandonment costs are accrued each period
based on the estimate of costs required to abandon the Trust's properties.
 
                                     --11--
<PAGE>   12
 
                          PART II.  OTHER INFORMATION
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.
 
  (a) Not applicable
 
  (b) Reports on Form 8-K:
 
      No reports on Form 8-K were filed by the registrant during the second
      quarter of 1997.
 
                                     --12--
<PAGE>   13
 
                                   SIGNATURE
 
     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.
 
                                  FREEPORT-McMoRan OIL AND GAS
                                  ROYALTY TRUST

                                  By: Texas Commerce Bank National Association,
                                        Trustee

                                  By:         /s/  PETE FOSTER
                                  --------------------------------------------
                                                   PETE FOSTER
                                     SENIOR VICE PRESIDENT AND TRUST OFFICER

Date: August 13, 1997
 
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                                EXHIBIT INDEX


            27 -- Financial Data Schedule