<PAGE>   1
 
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                                   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 March 31, 1999.
 
                                       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.)
 
   CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, TRUSTEE                            77002
                    712 MAIN STREET                                           (Zip Code)
                     HOUSTON, TEXAS
        (Address of principal executive offices)
</TABLE>
 
       Registrant's telephone number, including area code: (713) 216-5712
 
                      ....................................
 
   (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  ______
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<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...............    8
 
  Item 2.  Management's Discussion and Analysis of Financial
     Condition and Results of Operations....................    9
 
Part II.  Other Information
 
  Item 6.  Exhibits and Reports on Form 8-K.................    13
 
Signature...................................................    14
</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
                                                                      MARCH 31,
                                                              --------------------------
                                                                 1999           1998
                                                              -----------    -----------
<S>                                                           <C>            <C>
Royalty proceeds............................................  $        --    $        --
Trust administrative expenses...............................     (128,894)       (36,116)
Interest income.............................................       14,444         19,364
Reserve for future Trust expenses...........................      114,450         16,752
                                                              -----------    -----------
Distributable cash..........................................  $        --    $        --
                                                              ===========    ===========
Distributable cash per Unit.................................  $        --    $        --
                                                              ===========    ===========
Units outstanding...........................................   14,975,390     14,975,390
                                                              ===========    ===========
</TABLE>
 
               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
 
<TABLE>
<CAPTION>
                                                                MARCH 31,      DECEMBER 31,
                                                                  1999             1998
                           ASSETS                             -------------    -------------
<S>                                                           <C>              <C>
Cash and short-term investments.............................  $   1,292,153    $   1,406,603
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........................    (25,614,756)     (25,614,756)
Less, accumulated amortization of net overriding royalty
  interest..................................................   (164,260,985)    (164,260,985)
                                                              -------------    -------------
          Total assets......................................  $   1,292,153    $   1,406,603
                                                              =============    =============
                LIABILITIES AND TRUST CORPUS
Reserve for future Trust expenses...........................      1,292,153    $   1,406,603
Trust corpus (14,975,390 Units of Beneficial Interest
  authorized,
  issued and outstanding)...................................             --               --
                                                              -------------    -------------
          Total liabilities and trust corpus................  $   1,292,153    $   1,406,603
                                                              =============    =============
</TABLE>
 
                     STATEMENTS OF CHANGES IN TRUST CORPUS
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                                     MARCH 31,
                                                              -----------------------
                                                                1999         1998
                                                              --------    -----------
<S>                                                           <C>         <C>
Trust corpus, beginning of year.............................  $     --    $        --
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.................................  $     --    $        --
                                                              ========    ===========
</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 to a Partnership (the Partnership) a net overriding royalty interest
in certain offshore oil and gas properties 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 Chase Bank of Texas, 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 Trust
Indenture also provides that 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. There were no cash
receipts in 1996, 1997, and 1998 and, therefore, the terms of the Trust
Indenture dictate that the Trustee effect such a sale. However, the Unit holders
of the Trust, at a special meeting of the Unit holders held on March 12, 1999,
approved a Unit holder proposal to amend the Trust Indenture to extend the life
of the Trust for at least another two years. Any such amendment of the Trust
Indenture requires the written approval of the Trustee as well as approval of
the Unit holders. IMC Global Inc. (IMC), the successor to FTX's working
interests burdened by the Royalty, has filed a declaratory judgment action
seeking to prevent the Trustee from approving the amendment. The Trustee has
indicated that it will take no action to approve the amendment until such time
as the lawsuit is resolved. The Trustee will vigorously defend against the
lawsuit, but if IMC prevails in its lawsuit, the amendment will not be effected
and the Trustee will endeavor to sell the Royalty as soon as practicable for
cash to the highest bidder and terminate the Trust in accordance with the terms
of the Trust Indenture. See "Termination of the Trust." 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.
As of March 31, 1999, this Class A cost carry-forward was $26.5 million. This
cost carry-forward must be recouped by the Working Interest Owner before any
Royalty payment will be made to the Trust. There is no guarantee that the sale
of future production will result in proceeds in excess of the cost carry-forward
and other expenses. As a result, whether or not the Trust is terminated, there
may be no further Royalty payments to the Trust. Based on a study of the proved
oil and gas reserves attributable to the Royalty Properties as of December 31,
1998 made by Ryder Scott Company Petroleum Engineers (Ryder Scott), independent
petroleum engineers, there were no estimated proved oil and gas reserve
quantities or related discounted future
 
                                      --4--
<PAGE>   5
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
net cash flows attributable to the Trust at December 31, 1998. The Ryder Scott
estimates were prepared in accordance with regulations of the Securities and
Exchange Commission and were limited to reserves classified as "proved" as of
December 31, 1998. The Trust's Annual Report on Form 10-K includes a letter of
Ryder Scott relating to its estimates and information regarding the assumptions
used by Ryder Scott in preparing its reserve study. It also includes cautionary
paragraphs that should be studied carefully together with the estimates in the
letter.
 
2. THE ROYALTY
 
     IMC succeeded to FTX effective December 22, 1997, following the merger of
FTX into IMC. Accordingly, IMC is now the Working Interest Owner and 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,
including cost carry-forwards (Net Proceeds).
 
3. BASIS OF PRESENTATIONS
 
     The Trust's financial statements, which reflect the Trust's 99.9 percent
interest in the Partnership as though the Partnership did not exist, are
prepared on the cash basis of accounting for reporting revenues and expenses.
Therefore, revenues and expenses are recognized only as cash is received or paid
and the associated receivables, payables and accrued expenses are not reflected
in the accompanying financial statements. Under generally accepted accounting
principles, revenues and expenses would be recognized on an accrual basis.
 
     The initial carrying amount of the Royalty represented the Working Interest
Owner's net book value applicable to the interest in the properties conveyed to
the Trust on the date of creation of the Trust. Amortization of the Royalty has
been charged directly against trust corpus using the future net revenue method.
This method provides for calculating amortization by dividing the unamortized
portion of the Royalty by estimated future net revenues from proved reserves and
applying the resulting rate to the Trust's share of royalty proceeds.
 
     The carrying value of the Royalty is limited to the discounted present
value (at 10 percent) of estimated future net cash flows. Any excess carrying
value is reduced and the adjustment is charged directly against trust corpus.
The carrying value of the Royalty was $0 at March 31, 1999. Neither the initial
nor the March 31, 1999 carrying value is necessarily indicative of the fair
market value of the Royalty held by the Trust.
 
     Because the Trust is a grantor trust which is not a taxable entity, no
income taxes are reported in the Trust's financial statements. The tax
consequences of owning Units are included in the federal, state and local income
tax returns of the individual Unit holders.
 
                                      --5--
<PAGE>   6
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
4. DISTRIBUTIONS TO UNIT HOLDERS
 
     As a result of the capital cost incurred in recent years, a cumulative
excess Class A cost carry-forward of $26,490,669 existed as of March 31, 1999.
This carry-forward is subject to and includes an interest factor at the prime
rate, which totaled $561,709, net to the Trust during the three month period
ended March 31, 1999. This excess Class A cost carry-forward, including the
interest factor, must be recouped out of future Gross Proceeds before Royalty
payments to the Trust can be resumed.
 
5. 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 March 31, 1999, the unrecovered quantity of
gas sold by third parties pursuant to such gas balancing arrangements since
inception of the Trust was approximately 1.4 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.
 
6. 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 there is a
Class A cost deficit, the Trustee, in accordance with the Trust Indenture,
established an expense reserve of $2.4 million, of which $1,292,153 remained as
of March 31, 1999. Because of the cumulative excess Class A cost carry-forward
(Note 1), no Royalty payments were received, and $114,450 was withdrawn from the
expense reserve to pay Trust administrative expenses during the first three
months of 1999. There will be income tax consequences to the Unit holders for
such reserve as described in Note 7 below.
 
     The funding for this reserve is deposited with Chase Bank of Texas and
invested in Chase Bank of Texas collateralized certificates of deposit. The
average interest rate earned on these funds for the first quarter of 1999 was
4.3 percent.
 
7. FEDERAL INCOME TAX MATTERS
 
     Unit holders are required to report taxable income for any Royalty income
received by the Trust and interest on the Trust's cash reserves, even if no
distributions are received by the Unit holders. Unit holders will
 
                                      --6--
<PAGE>   7
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
have future income tax deductions as additional administrative expenses are
incurred and paid with funds deposited in the expense reserve established for
Trust administrative expenses described in Note 6 above.
 
8. RESERVE FOR FUTURE ABANDONMENT COSTS
 
     Estimated future abandonment costs are accrued over the life of the Trust's
properties based on current laws and regulations. Such 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 or
technology. As of December 31, 1998, the estimated remaining aggregate
abandonment costs to be incurred for all of the Trust's properties totaled $9.5
million net to the Trust, all of which has been withheld from distributions to
the Trust. Any further adjustments to estimated abandonment costs or variances
to actual costs will reduce or increase Net Proceeds accordingly.
 
9. SUBSEQUENT EVENTS
 
Transportation Agreement
------------------------
 
     In December 1997 the Working Interest Owner entered into a crude oil
agreement with an oil pipeline company to deliver on a daily basis specified
quantities of crude oil from West Cameron 498. Under the terms of the agreement
the Working Interest Owner agreed to pay a transportation fee calculated at a
sliding monthly rate based upon the total average daily volumes delivered from
West Cameron 498 during the month. Should the annual minimum delivery volume not
be met a deficiency payment is assessed by the pipeline. During 1998 the Working
Interest Owner did not deliver the minimum volume under the agreement.
Therefore, in February 1999 the pipeline company billed the Working Interest
Owner approximately $687,000 for the 1998 deficiency. The amount paid will be
included in cost carry-forward in 1999. The minimum volume, net to the Working
Interest Owner for 1999 will be 697,000 barrels, declining to 126,449 barrels in
2007. Based on the Working Interest Owner's estimate of 1999 production the
minimum delivery volumes will not be met in 1999. However should production
exceed the 1999 minimum, the Working Interest Owner is entitled to receive
transportation without pay up to the cumulative prior underdelivered volumes.
The Working Interest Owner is in discussions with the oil pipeline company
concerning a renegotiation of the agreement and approximately $600,000 will be
included in the Class A cost carryforward in April, 1999.
 
Insurance Accrual
-----------------
 
     In April, 1999 the Working Interest Owner's insurer requested repayment of
approximately $240,000 in worker's compensation insurance proceeds paid to the
Working Interest Owner in November 1998. The proceeds related to the applicable
deductible for a claim occurring on the Vermilion 310 property, and were
reflected as a reduction of previously incurred Class A costs in 1998.
Accordingly, an accrual for $240,000 will be included in the Class A cost
carryforward related to reimbursement of these proceeds in the second quarter of
1999.
 
                             ---------------------
 
                                      --7--
<PAGE>   8
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
     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, 1998, WHICH ARE CONTAINED IN ITS ANNUAL REPORT ON FORM 10-K
FOR 1998.
 
                                      --8--
<PAGE>   9
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
 
                    REPORT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
To Chase Bank of Texas 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 March 31, 1999,
the related statements of royalty proceeds and distributable cash and changes in
trust corpus for the three month periods ended March 31, 1999 and 1998. 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.
 
     As discussed in Note 3, 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, 1998 and, in our
report dated April 5, 1999, we expressed an unqualified opinion on that
statement.
 
                                          ARTHUR ANDERSEN LLP
 
New Orleans, Louisiana
May 11, 1999
 
                                      --9--
<PAGE>   10
 
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 oil and
gas reserves, government regulations and other matters beyond the control of the
Trustee and the Working Interest Owner.
 
     The Trust Indenture provides that the Trustee must sell the Trust's
interest in the Partnership, or cause the Partnership to sell the Royalty, if
the Trust receives less than $3 million in cash in each of three consecutive
years. The Trust received no cash in 1996, 1997 or 1998. Therefore, unless the
amendment of the Trust Indenture approved by the Unit holders is effected, the
Trustee will endeavor to effect such sale. At a special meeting of the Unit
holders held on March 12, 1999, the Unit holders of the Trust approved a Unit
holder proposal to amend the Trust Indenture to extend the life of the Trust for
at least another two years. Any such amendment of the Trust Indenture requires,
in addition to the requisite vote of the Unit holders, the written approval of
the Trustee. The Working Interest Owner has filed a declaratory judgment action
seeking to enjoin the Trustee from approving the amendment. The Trustee will
take no action to approve the amendment until such time as the lawsuit is
resolved. The Trustee will vigorously defend against the lawsuit, but if the
Working Interest Owner prevails in its lawsuit, the amendment will not be
effected and the Trustee will endeavor to sell the Royalty as soon as
practicable for cash to the highest bidder and terminate the Trust in accordance
with the terms of the Trust Indenture. Although the Trustee will endeavor to
offer the Royalty pursuant to procedures intended to maximize the proceeds to
the Trust, the Trustee can give no assurance regarding the amounts, if any, to
be realized as a result of such offer. It is the Trustee's intention to approve
the amendment if the lawsuit is resolved in a manner that permits the Trustee to
do so.
 
OPERATIONAL ACTIVITIES
 
     There was no exploratory or development activity on the properties during
the first three months of 1999. Oil production on West Cameron 498 rapidly
declined during the first three months of 1999. This is due primarily to
mechanical and well performance on one well. However the operator will conduct
remedial action to attempt to return the field to production expectations. This
remedial action is expected to occur during the second quarter of 1999.
 
                                     --10--
<PAGE>   11
 
RESULTS OF OPERATIONS
 
     There were no cash distributions to the Unit holders during the first three
months of 1999 or 1998. During the first quarter of 1999, Total Costs exceeded
Gross Proceeds by approximately $1.0 million. As a result, the Class A cost
carry-forward increased to $26.4 million (Note 3) net to the Trust as of March
31, 1999. Because of the Class A cost carry-forward, Trust administrative
expenses were paid from the expense reserve during the 1999 and 1998 periods.
The calculation of distributable cash for each period follows:
 
<TABLE>
<CAPTION>
                                                                  THREE MONTHS ENDED
                                                                      MARCH 31,
                                                              --------------------------
                                                                 1999           1998
                                                              -----------    -----------
<S>                                                           <C>            <C>
Gross Proceeds(1)...........................................  $ 1,251,135    $   764,281
Total Costs(2)..............................................   (2,211,884)    (4,111,067)
Excess Class A cost carry-forward, net(3)...................      960,749      3,346,786
                                                              -----------    -----------
Net Proceeds................................................           --             --
Percentage attributable to Royalty..........................         90.0%          90.0%
                                                              -----------    -----------
Amounts payable attributable to Royalty.....................           --             --
Percentage attributable to the Trust........................         99.9%          99.9%
                                                              -----------    -----------
Royalty Proceeds............................................           --             --
Trust administrative expenses...............................     (128,894)       (36,116)
                                                              -----------    -----------
                                                                 (128,894)       (36,116)
Interest income.............................................       14,444         19,364
Reserve for future Trust expenses(4)........................      114,450         16,752
                                                              -----------    -----------
Distributable cash..........................................  $        --    $        --
                                                              ===========    ===========
</TABLE>
 
---------------
 
(1) Represents amounts received by the Working Interest Owner during the three
     month period ended in February of such year.
 
(2) Represents amounts accrued by the Working Interest Owner during the three
     month period ended in February of such year. Includes accrued interest of
     $561,709 in 1999 and $366,303 in 1998.
 
(3) Represents Class A costs incurred in the applicable period that remained
     outstanding as of the end of such period.
 
(4) Represents withdrawals from the Trust administrative expense reserve during
     the respective periods.
 
                                     --11--
<PAGE>   12
 
     Gross Proceeds, which include gas and oil revenues, are calculated based on
amounts received by the Working Interest Owner. Operating information follows:
 
<TABLE>
<CAPTION>
                                                                  FIRST QUARTER
                                                              ---------------------
                                                                1999         1998
                                                              --------     --------
<S>                                                           <C>          <C>
Natural Gas
  Revenues (in millions)....................................   $  0.7       $  0.7
  Sales volumes (in million cubic feet).....................      405          249
  Average realization (per thousand cubic feet).............   $ 1.77       $ 2.74
Oil
  Revenues (in millions)....................................   $  0.5       $  0.1
  Sales volumes (in thousands of barrels)...................     49.2          4.3
  Average realization (per barrel)..........................   $18.83       $19.38
</TABLE>
 
     Both oil and gas volumes for the first three months of 1999 period
increased significantly over the 1998 period because of the commencement of
production at West Cameron Block 498. The new production at West Cameron Block
498 was offset in part by normal production declines on the remaining
properties.
 
     Costs consist of the following (in millions):
 
<TABLE>
<CAPTION>
                                                                  FIRST QUARTER
                                                              ---------------------
                                                                1999         1998
                                                              --------     --------
<S>                                                           <C>          <C>
Lease operating expenses....................................    $0.8         $0.4
Exploration and development costs...........................     0.8          3.2
Interest, abandonment costs withheld and other..............     0.6          0.5
                                                                ----         ----
                                                                $2.2         $4.1
                                                                ====         ====
</TABLE>
 
     Lease operating expenses for the 1999 period increased over the 1998 period
because of increased lease operating expense for West Cameron Block 498 during
the period. Development costs for the first quarter 1999 relate primarily to
development at West Cameron Block 498. First quarter 1998 costs also related to
the development of West Cameron Block 498.
 
     In December 1997 the Working Interest Owner entered into a crude oil
agreement with an oil pipeline company to deliver on a daily basis specified
quantities of crude oil from West Cameron 498. Under the terms of the agreement
the Working Interest Owner agreed to pay a transportation fee calculated at a
sliding monthly rate based upon the total average daily volumes delivered from
West Cameron 498 during the month. Should the annual minimum delivery volume not
be met a deficiency payment is assessed by the pipeline. During 1998 the Working
Interest Owner did not deliver the minimum volume under the agreement.
Therefore, in February 1999 the pipeline company billed the Working Interest
Owner approximately $687,000 for the 1998 deficiency. The amount paid will be
included in cost carry-forward in 1999. The minimum volume, net to the Working
Interest Owner for 1999 will be 697,000 barrels, declining to 126,449 barrels in
2007. Based on the Working Interest Owner's estimate of 1999 production the
minimum delivery volumes will not be met in 1999. However should production
exceed the 1999 minimum, the Working Interest Owner is entitled to receive
transportation without pay up to the cumulative prior underdelivered volumes.
The Working
 
                                     --12--
<PAGE>   13
 
Interest Owner is in discussions with the oil pipeline company concerning a
renegotiation of the agreement and approximately $600,000 of this was accrued in
April, 1999.
 
     In April, 1999 the Working Interest Owner's insurer requested repayment of
approximately $240,000 in worker's compensation insurance proceeds paid to the
Working Interest Owner in November 1998. The proceeds related to the applicable
deductible for a claim occurring on the Vermilion 310 property, and were
reflected as a reduction of previously incurred Class A costs in 1998.
Accordingly, an accrual for $240,000 will be included in the Class A cost
carryforward related to reimbursement of these proceeds in the second quarter of
1999.
 
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 the Unit holders, upon termination of the Trust
and in certain other limited circumstances. However, the Trust is directed to
effect such a sale (without 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 Unit holders have approved an amendment to the Trust
Indenture to extend the life of the Trust for at least another two years, but
such amendment has not become effective because of pending litigation. See Note
1 to the Trust's financial statements included elsewhere in this report.
 
     The Trust's cash receipts last reached $3 million during 1995, and there
were no cash receipts in 1996, 1997 or 1998. Additionally, the Class A cost
carry-forward has increased to $26.5 million at March 31, 1999, primarily from
the significant development costs incurred at West Cameron Blocks 498 (Note 3).
This cost carry-forward must be recouped by the Working Interest Owner before
any distribution may be made to the Trust. Since the Trust did not receive cash
receipts of at least $3 million during 1998, the Trust will be terminated by one
of the means described under "Termination of the Trust" above, unless the
amendment to the Trust Indenture approved by the Unitholders on March 12, 1999
is implemented.
 
     Additional exploration may be proposed by the operators of certain other
Royalty Properties. After analyzing each proposal, the Working Interest Owner
will determine whether or not to participate in additional exploratory
operations.
 
     The operators have not presented the Working Interest Owner with any
further exploration or development plans for 1999. Therefore, there are no
additional exploration and development costs budgeted for 1999. However the
operator of West Cameron 498 will conduct remedial action to attempt to return
the field to production expectations, and has submitted an AFE for approximately
$60,000 net to the Working Interest Owner.
 
     Estimated future abandonment costs, based on current laws and regulations,
are accrued over the life of the Trust's properties (Note 8). As of March 31,
1999, the estimated remaining aggregate abandonment costs to be incurred for all
of the Trust's properties totaled $9.5 million net to the Trust, of which all
has been withheld from distributions to Unit holders. Any adjustments to the
estimated abandonment costs or variances will reduce or increase future Net
Proceeds accordingly.
 
                                     --13--
<PAGE>   14
 
     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 6), of which $1.3
million remained at March 31, 1999.
 
                          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 with the Securities and Exchange
      Commission during the first quarter of 1999.
 
                                     --14--
<PAGE>   15
 
                                   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.
 
<TABLE>
<S>                                                      <C>
                                                         FREEPORT-McMoRan OIL AND GAS
                                                         ROYALTY TRUST
 
                                                         By: Chase Bank of Texas, National
                                                         Association,
                                                               Trustee
 
                                                                      By:/s/ PETE FOSTER
                                                         ---------------------------------------------
                                                                          PETE FOSTER
                                                            SENIOR VICE PRESIDENT AND TRUST OFFICER
</TABLE>
 
Date: May 14, 1999
 
                                     --15--
<PAGE>   16
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                       DESCRIPTION
         ------                                       -----------
<C>                           <S>
           27                 Financial Data Schedule
</TABLE>