<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549



                                    Form 10-Q



                Quarterly Report Pursuant to Section 13 or 15(d)
                     of the Securities Exchange Act of 1934



                For the Quarterly Period Ended September 30, 1998


                           Commission File No. 1-8032



                          SAN JUAN BASIN ROYALTY TRUST


   Texas                                                  I.R.S. No. 75-6279898


                Bank One, Texas, N.A., Corporate Trust Department
                                 P. O. Box 2604
                             Fort Worth, Texas 76113

                          Telephone Number 817/884-4630


Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months and (2) has been subject to such filing requirements for
the past 90 days. Yes X No
                     ---     ---

Number of units of beneficial interest outstanding at November 14, 1998:
46,608,796


                                  Page 1 of 14
<PAGE>   2


                          SAN JUAN BASIN ROYALTY TRUST

                         PART I - FINANCIAL INFORMATION


ITEM 1.   FINANCIAL STATEMENTS.

The condensed financial statements included herein have been prepared by Bank
One, Texas, N.A. as Trustee for the San Juan Basin Royalty Trust, without audit,
pursuant to the rules and regulations of the Securities and Exchange Commission.
Certain information and footnote disclosures normally included in annual
financial statements have been condensed or omitted pursuant to such rules and
regulations, although the Trustee believes that the disclosures are adequate to
make the information presented not misleading. It is suggested that these
condensed financial statements be read in conjunction with the financial
statements and the notes thereto included in the Trust's latest annual report on
Form 10-K. In the opinion of the Trustee, all adjustments, consisting only of
normal recurring adjustments, necessary to present fairly the assets,
liabilities and trust corpus of the San Juan Basin Royalty Trust at September
30, 1998, and the distributable income and changes in trust corpus for the
three-month and nine-month periods ended September 30, 1998 and 1997 have been
included. The distributable income for such interim periods is not necessarily
indicative of the distributable income for the full year.

Deloitte & Touche LLP, independent certified public accountants, has made a
limited review of the condensed financial statements as of September 30, 1998
and for the three-month and nine-month periods ended September 30, 1998 and 1997
included herein.

                                      -2-

<PAGE>   3




INDEPENDENT ACCOUNTANTS' REPORT


Bank One, Texas, N.A. as Trustee for the
   San Juan Basin Royalty Trust:

We have reviewed the accompanying condensed statement of assets, liabilities and
trust corpus of the San Juan Basin Royalty Trust as of September 30, 1998 and
the related condensed statements of distributable income and changes in trust
corpus for the three-month and nine-month periods ended September 30, 1998 and
1997. These financial statements are the responsibility of the Trustee.

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 procedures to
financial data and making inquiries of persons responsible for financial and
accounting matters. It is substantially less in scope than an audit conducted 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.

The accompanying condensed financial statements are prepared on a modified cash
basis as described in Note 1, 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 such condensed financial statements for them to be in conformity with
the basis of accounting described in Note 1.

We have previously audited, in accordance with generally accepted auditing
standards, the statement of assets, liabilities and trust corpus of the San Juan
Basin Royalty Trust as of December 31, 1997, and the related statements of
distributable income and changes in trust corpus for the year then ended (not
presented herein); and in our report dated March 25, 1998, we expressed an
unqualified opinion on those financial statements. In our opinion, the
information set forth in the accompanying condensed statement of assets,
liabilities and trust corpus as of December 31, 1997 is fairly stated in all
material respects, in relation to the statement of assets, liabilities and trust
corpus from which it has been derived.


DELOITTE & TOUCHE LLP

October 21, 1998


                                      -3-
<PAGE>   4


SAN JUAN  BASIN ROYALTY TRUST

CONDENSED STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>

                                                          SEPTEMBER 30,   DECEMBER 31,
ASSETS                                                       1998             1997
                                                          (UNAUDITED)

<S>                                                       <C>             <C>        
Cash and short-term investments                           $ 2,210,715     $ 5,111,832
Net overriding royalty interests in producing oil and
  gas properties (net of accumulated amortization of
  $81,032,927 and $77,156,080 at September 30, 1998
  and December 31, 1997, respectively)                     52,242,601      56,119,448
                                                          -----------     -----------

                                                          $54,453,316     $61,231,280
                                                          ===========     ===========
LIABILITIES AND TRUST CORPUS

Distribution payable to Unit holders                      $ 2,210,715     $ 5,111,832
Trust corpus - 46,608,796 Units of beneficial
   interest authorized, issued and outstanding             52,242,601      56,119,448
                                                          -----------     -----------

                                                          $54,453,316     $61,231,280
                                                          ===========     ===========
</TABLE>

CONDENSED STATEMENTS OF DISTRIBUTABLE INCOME (UNAUDITED)
--------------------------------------------------------------------------------
<TABLE>
<CAPTION>

                                       THREE MONTHS ENDED              NINE MONTHS ENDED
                                          SEPTEMBER 30,                  SEPTEMBER 30,
                                  ---------------------------     ---------------------------

                                       1998           1997           1998            1997

<S>                               <C>             <C>             <C>             <C>        
Royalty income                    $ 6,276,679     $ 9,763,541     $24,618,472     $37,134,776
Interest income                        12,749          21,669          57,951          76,214
                                  -----------     -----------     -----------     -----------
                                    6,289,428       9,785,210      24,676,423      37,210,990

General and administrative
   expenditures                       125,509         180,243         663,603         773,496
                                  -----------     -----------     -----------     -----------

Distributable income              $ 6,163,919     $ 9,604,967     $24,012,820     $36,437,494
                                  ===========     ===========     ===========     ===========

Distributable income per Unit
   (46,608,796 Units)             $   .132248     $   .206076     $   .515199     $   .781772
                                  ===========     ===========     ===========     ===========
</TABLE>

The accompanying notes to condensed financial statements are an integral part of
these statements.

                                      -4-
<PAGE>   5

SAN JUAN BASIN ROYALTY TRUST

CONDENSED STATEMENTS OF CHANGES IN TRUST CORPUS  (UNAUDITED)
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>

                                            THREE MONTHS ENDED                  NINE MONTHS ENDED
                                               SEPTEMBER 30,                      SEPTEMBER 30,
                                      ------------------------------      ------------------------------

                                           1998              1997             1998               1997

<S>                                   <C>               <C>               <C>               <C>         
Trust corpus, beginning of period     $ 53,419,624      $ 59,227,104      $ 56,119,448      $ 62,808,148
Amortization of net overriding
   royalty interest                     (1,177,023)       (1,546,656)       (3,876,847)       (5,127,700)
Distributable income                     6,163,919         9,604,967        24,012,820        36,437,494
Distributions declared                  (6,163,919)       (9,604,967)      (24,012,820)      (36,437,494)
                                      ------------      ------------      ------------      ------------

Trust corpus, end of period           $ 52,242,601      $ 57,680,448      $ 52,242,601      $ 57,680,448
                                      ============      ============      ============      ============
</TABLE>


The accompanying notes to condensed financial statements are an integral part of
these statements.

                                      -5-
<PAGE>   6
SAN JUAN BASIN ROYALTY TRUST

NOTES TO CONDENSED FINANCIAL STATEMENTS (UNAUDITED)
--------------------------------------------------------------------------------


1.    BASIS OF ACCOUNTING

      The San Juan Basin Royalty Trust ("Trust") was established as of November
      1, 1980. The financial statements of the Trust are prepared on the
      following basis:

      o    Royalty income recorded for a month is the amount computed and paid
           by the working interest owner, Burlington Resources Oil & Gas Company
           ("BROG"), to the Trustee for the Trust. Royalty income consists of
           the amounts received by the owner of the interest burdened by the net
           overriding royalty interest ("Royalty") from the sale of production
           less accrued production costs, development and drilling costs,
           applicable taxes, operating charges, and other costs and deductions,
           multiplied by 75%.

      o    Trust expenses recorded are based on liabilities paid and cash
           reserves established from royalty income for liabilities and
           contingencies.

      o    Distributions to Unit holders are recorded when declared by the
           Trustee.

      o    The conveyance which transferred the overriding royalty interest to
           the Trust provides that any excess of production costs over gross
           proceeds must be recovered from future net profits.

      The financial statements of the Trust differ from financial statements
      prepared in accordance with generally accepted accounting principles
      ("GAAP") because revenues are not accrued in the month of production;
      certain cash reserves may be established for contingencies which would not
      be accrued in financial statements prepared in accordance with GAAP; and
      amortization of the Royalty calculated on a unit-of-production basis is
      charged directly to trust corpus.

2.    FEDERAL INCOME TAXES

      For federal income tax purposes, the Trust constitutes a fixed investment
      trust which is taxed as a grantor trust. A grantor trust is not subject to
      tax at the trust level. The Unit holders are considered to own the Trust's
      income and principal as though no trust were in existence. The income of
      the Trust is deemed to have been received or accrued by each Unit holder
      at the time such income is received or accrued by the Trust rather than
      when distributed by the Trust.

      The Royalty constitutes an "economic interest" in oil and gas properties
      for federal income tax purposes. Unit holders must report their share of
      the revenues of the Trust as ordinary income from oil and gas royalties
      and are entitled to claim depletion with respect to such income. The
      Royalty is treated as a single property for depletion purposes.

      The Trust has on file technical advice memoranda confirming the tax
      treatment described above.

      The Trust began receiving royalty income from coal seam wells beginning in
      1989. Under Section 29 of the Internal Revenue Code, production from coal
      seam gas wells drilled prior to January 1, 1993, qualifies for the federal
      income tax credit for producing non-conventional fuels. This tax credit
      was approximately $1.05 per MMBtu for the year 1997 and is adjusted for
      inflation annually. The credit currently applies to production through the
      year 2002. Production from wells drilled after December 31, 1979, but
      prior to January 1, 1993, to a formation beneath a qualifying coal seam

                                      -6-
<PAGE>   7

      formation which are later completed into such formation also qualifies for
      the tax credit. Each Unit holder must determine his pro rata share of such
      production based upon the number of Units owned during each month of the
      year and apply the tax credit against his own income tax liability, but
      such credit may not reduce his regular tax liability (after the foreign
      tax credit and certain other nonrefundable credits) below his tentative
      minimum tax. Section 29 also provides that any amount of Section 29 credit
      disallowed for the tax year solely because of this limitation will
      increase his credit for prior year minimum tax liability, which may be
      carried forward indefinitely as a credit against the taxpayer's regular
      tax liability, subject, however, to the limitations described in the
      preceding sentence. There is no provision for the carryback or
      carryforward of the Section 29 credit in any other circumstances.

      The Trustee is provided Section 29 tax credit information related to Trust
      Properties by BROG. In 1997, the Tax Court upheld the IRS position that
      nonconventional fuel such as coal seam gas does not qualify for the
      Section 29 credit unless the producer received a formal certification from
      the Federal Energy Regulatory Commission ("FERC"). The FERC's
      certification authority expired effective January 1, 1993. Many producers
      believe that wells meeting the certification requirements are eligible for
      the Section 29 credit regardless of FERC certification. However, this
      position is not in accordance with the IRS position or the decision of the
      Tax Court. The court decision is on appeal and it is not possible to
      predict the likely outcome. In the event the appeal is not successful, the
      ability of the Unit holders to utilize allocated Section 29 credits in
      full could be in question.

      The classification of the Trust's income for purposes of the passive loss
      rules may be important to a Unit holder. As a result of the Tax Reform Act
      of 1986, royalty income will generally be treated as portfolio income and
      will not reduce passive losses.

3.    CONTINGENCIES

      See Item 1 Legal Proceedings concerning the status of litigation matters.

                                     ******

                                      -7-
<PAGE>   8



ITEM 2.  TRUSTEE'S DISCUSSION AND ANALYSIS

FORWARD LOOKING INFORMATION

Certain information included in this report contains, and other materials filed
or to be filed by the Trust with the Securities and Exchange Commission (as well
as information included in oral statements or other written statements made or
to be made by the Trust) may contain or include, forward looking statements
within the meaning of Section 21E of the Securities Exchange Act of 1934, as
amended, and Section 27A of the Securities Act of 1933, as amended. Such forward
looking statements may be or may concern, among other things, capital
expenditures, drilling activity, development activities, production efforts and
volumes, hydrocarbon prices and the results thereof, and regulatory matters.
Such forward looking statements generally are accompanied by words such as
"estimate," "expect," "predict," "anticipate," "goal," "should," "assume,"
"believe," or other words that convey the uncertainty of future events or
outcomes.

YEAR 2000 ISSUE

Many existing computer programs use only two digits to identify a year in the
date field. These programs were designed and developed without considering the
impact of the upcoming change in the century. If not corrected, many computer
applications could fail or create erroneous results by the Year 2000. The Year
2000 issue affects virtually all companies and organizations. If a company or
organization does not successfully address its Year 2000 issues, it may face
material adverse consequences.

As the Trust does not directly maintain any systems, the Trust will not incur
any direct costs related to the Year 2000 issue. However, the Trust is reliant
on the performance of others, including the Trustee, BROG and third party
vendors (collectively, the "suppliers") for such things as the calculation and
receipt of Royalty income, payment of expenses and disbursement of distributable
income. The Trust has made formal inquiries to the suppliers requesting
information on their state of readiness for the Year 2000. The Trust is awaiting
a response from BROG. Based upon responses received and reviewed by the Trust
with respect to its other material suppliers, all are currently addressing the
Year 2000 issue and making efforts to be compliant prior to the Year 2000. The
Trust can provide no assurance as to whether the suppliers will successfully
address the Year 2000 issue. Failure to successfully address the Year 2000 issue
by the suppliers could have a material adverse impact on the Trust and its Unit
holders. At this time, the Trust believes the most adverse impact as a result of
the suppliers' failure to successfully address the Year 2000 issue is that the
Trust would not receive and in turn would not be able to distribute royalty
income to the Unit holders.

THREE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

The San Juan Basin Royalty Trust received royalty income of $6,276,679 and
interest income of $12,749 during the third quarter of 1998. After deducting
administrative expenses of $125,509, distributable income for the third quarter
was $6,163,919 ($.132248 per Unit). In the third quarter of 1997, royalty income
was $9,763,541, interest income was $21,669, administrative expenses were
$180,243 and distributable income was $9,604,967 ($.206076 per Unit). The tax
credit relating to production from coal seam wells totaled approximately $.04
per Unit for the third quarter of 1998 and $.05 per Unit for the third quarter
of 1997. For further information concerning this tax credit, Unit holders should
refer to the Trust's Annual Report for 1997. Based on 46,608,796 Units
outstanding, the per Unit distributions during the third quarter of 1998 were as
follows:
<TABLE>

<S>                                     <C>      
July                                    $ .046990
August                                    .037827
September                                 .047431
                                          -------

Quarter Total                           $ .132248
                                        =========
</TABLE>

                                      -8-
<PAGE>   9

The royalty income distributed in the third quarter of 1998 was lower than that
distributed in the third quarter of 1997, primarily due to a decrease in the
average gas price from $1.76 per Mcf for the third quarter of 1997 to $1.62 per
Mcf for the third quarter of 1998 and to an increase in capital costs during the
third quarter of 1998. Interest earnings for the quarter ended September 30,
1998, as compared to the quarter ended September 30, 1997, were lower, primarily
due to decreased funds available for investment. Administrative expenses
decreased, primarily as a result of differences in timing of the receipt and
payment of these expenses and lower consulting and audit expenses.

The capital costs attributable to the properties from which the Royalty was
carved (the "Underlying Properties") for the third quarter of 1998 were reported
by BROG as $3,745,082 versus $1,537,795 for the third quarter of 1997. BROG
indicates that the majority of the increase in capital expenditures is
attributable to conventional projects, but that based on its success in 1997,
significant capital will be allocated to increasing the density and productivity
of its operations in the Fruitland Coal. BROG has informed the Trustee that its
estimated capital budget for 1998 has been increased from $10 million to $10.9
million. Lease operating expenses and property taxes were $2,786,500 for the
third quarter of 1998 as compared to $2,649,405 for the third quarter of 1997.

BROG has informed the Trustee that during the third quarter of 1998, 1 gross
(.04 net) conventional well was completed on the Underlying Properties. There
were 36 gross (7.70 net) conventional wells in progress at September 30, 1998.
Two gross (1.47 net) conventional wells were recompleted and 5 gross (.21 net)
coal seam well recavitations were completed on the Underlying Properties in the
third quarter of 1998. Two gross (.07 net) conventional well recompletions, 1
gross (.045 net) coal seam recompletions and 5 gross (.16 net) coal seam
recavitations were in progress at September 30, 1998. By comparison, twelve
gross (.60 net) conventional wells were completed on the Underlying Properties
in the third quarter of 1997. There were 1 gross (.04 net) coal seam and 29
gross (2.4 net) conventional wells in progress at September 30, 1997. Three
gross (1.76 net) conventional wells were recompleted through September 30, 1997.
Five gross (1.15 net) conventional well recompletions and twelve gross (.46 net)
coal seam recompletions were in progress as of September 30, 1997. Six gross
(1.01 net) coal seam well recavitations were completed and nine gross (.71) net
coal seam well recavitations were in progress as of September 30, 1997. Unit
holders are referred to "Description of the Properties" in the Trust's Annual
Report for 1997 for further information concerning BROG's coal seam gas well
drilling program in the San Juan Basin. This program includes properties in
which the Trust owns an interest.

Royalty income for the quarter ended September 30, 1998 is associated with
actual gas and oil production during May 1998 through July 1998 from the
Underlying Properties. Gas and oil sales from the Underlying Properties for the
quarters ended September 30, 1998 and 1997 were as follows:

<TABLE>
<CAPTION>

                                 1998             1997
<S>                           <C>            <C>       
Gas:
  Total sales (Mcf)           10,135,621     10,679,663
  Mcf per day                    110,170        116,083
  Average price (per Mcf)     $     1.62     $     1.76

Oil:
  Total sales (Bbls)              18,478         21,568
  Bbls per day                       201            234
  Average price (per Bbl)     $    12.03     $    17.67
</TABLE>

                                      -9-
<PAGE>   10

Gas and oil sales attributable to the Royalty for the quarters ended September
30, 1998 and 1997 were as follows:

<TABLE>
<CAPTION>

                                                 1998               1997

<S>                                           <C>                <C>      
Gas sales (Mcf)                               4,264,729          6,057,651
Oil sales (Bbls)                                  7,771             12,247
</TABLE>

During the third quarter of 1998, gas prices were lower than during the third
quarter of 1997. Gas production also decreased in 1998 as compared to 1997. The
price per barrel of oil during the third quarter of 1998 was $5.64 per bbl lower
than that received for the third quarter of 1997 due to decreases in oil prices
in world markets generally including the posted prices applicable to oil sales
attributable to the Royalty.

Since the oil and gas sales attributable to the Royalty are based on an
allocation formula that is dependent on such factors as price and cost,
including capital expenditures, the aggregate production volumes from the
Underlying Properties may not provide a meaningful comparison to volumes
attributable to the Royalty.

Effective January 1, 1998, all volumes of Trust gas became subject to the terms
of a Natural Gas Sales and Purchase Contract between BROG and El Paso Energy
Marketing Company ("El Paso"). That contract is for a term of two years through
and including December 31, 1999, and provides for the sale of Trust gas at
prices which will fluctuate in accordance with published indices for gas sold in
the San Juan Basin of New Mexico. BROG entered into the contract with El Paso
after soliciting and receiving competitive bids in late 1997 from six major gas
marketing firms to market and/or purchase the Trust gas. Unit holders are
referred to Note 6 of the Notes to Financial Statements in the Trust's 1997
Annual Report for further information concerning the marketing of gas produced
from the Underlying Properties.

NINE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

For the nine months ended September 30, 1998, distributable income was
$24,012,820 ($.515199 per Unit), which was less than the $36,437,494 ($.781772
per Unit) of income distributed during the same period in 1997. The decrease
resulted primarily from decreases in gas and oil prices. Interest income for the
nine months ended September 30, 1998 was $57,951 compared to $76,214 during the
first nine months of 1997. This decrease is due to a decrease in funds available
for investment. General and administrative expenses decreased to $663,603 from
$773,496 during the 1997 period primarily due to differences in timing of the
receipt and payment of these expenses.

Capital expenditures incurred by BROG, attributable to the Underlying
Properties, for the first nine months of 1998 amounted to $10,048,168. Capital
expenditures were $5,651,763 for the first nine months of 1997.

Lease operating expenses and property taxes totaled $8,590,061 for the first
nine months of 1998 compared to $8,303,522 for the first nine months of 1997.


                                      -10-
<PAGE>   11



BROG informed the Trustee that during the nine months ended September 30, 1998,
10 gross (5.13 net) conventional wells were completed on the Underlying
Properties and 21 gross (10.74 net) conventional wells were recompleted.
Twenty-nine gross (2.01 net) coal seam wells were recavitated during the first
nine months of 1998. During the nine months ended September 30, 1997, 41 gross
(2.66 net) conventional wells were completed on the Underlying Properties.
One gross (.84 net) coal seam and four gross (2.59 net) conventional wells were
recompleted during the first nine months of 1997. Ten gross (1.56 net) coal seam
wells were recavitated during the first nine months of 1997.

Royalty income for the nine months ended September 30, 1998 is associated with
actual gas and oil production during November 1997 through July 1998 from the
Underlying Properties. Gas and oil sales from the Underlying Properties for the
nine months ended September 30, 1998 and 1997 were as follows:

<TABLE>
<CAPTION>

                                  1998          1997
<S>                           <C>            <C>       
Gas:
  Total sales (Mcf)           31,263,993     31,506,749
  Mcf per day                    114,520        115,409
  Average price (per Mcf)     $     1.81     $     2.19

Oil:
  Total sales (Bbls)              63,694         70,054
  Bbls per day                       233            257
  Average price (per Bbl)     $    13.80     $    19.70
</TABLE>


Gas and oil sales attributable to the Royalty for the nine months ended
September 30, 1998 and 1997 were as follows:

<TABLE>
<CAPTION>

                                  1998           1997

<S>                           <C>            <C>       
Gas sales (Mcf)               14,721,489     18,122,585
Oil sales (Bbls)                  29,706         39,460
</TABLE>

During the first nine months of 1998, gas and oil prices were lower than during
the first nine months of 1997. Since the oil and gas sales attributable to the
Royalty are based on an allocation formula that is dependent on such factors as
price and cost, including capital expenditures, the aggregate sales amounts from
the Underlying Properties may not provide a meaningful comparison to sales
attributable to the Royalty.


                                      -11-
<PAGE>   12



CALCULATION OF ROYALTY INCOME:

Royalty income received by the Trust for the three months and nine months ended
September 30, 1998 and 1997, respectively, was computed as shown in the
following table:

<TABLE>
<CAPTION>

                                      THREE MONTHS ENDED             NINE MONTHS ENDED
                                        SEPTEMBER 30,                  SEPTEMBER 30,
                                -----------------------------------------------------------
                                    1998           1997            1998            1997
<S>                             <C>             <C>             <C>             <C>        
Gross proceeds of sales from 
  the Underlying Properties:

   Gas proceeds                 $16,436,207     $18,758,331     $56,513,251     $69,003,247
   Oil proceeds                     222,230         381,186         879,060       1,380,372
                                -----------     -----------     -----------     -----------

           Total                 16,658,437      19,139,517      57,392,311      70,383,619
                                -----------     -----------     -----------     -----------

Less production costs:
   Severance tax - Gas            1,735,847       1,896,788       5,832,736       6,782,548
   Severance tax - Oil               22,103          37,474          96,716         132,751
   Lease operating expenses
      and property tax            2,786,500       2,649,405       8,590,061       8,303,522
   Capital expenditures           3,745,082       1,537,795      10,048,169       5,651,763
                                -----------     -----------     -----------     -----------

           Total                  8,289,532       6,121,462      24,567,682      20,870,584
                                -----------     -----------     -----------     -----------

Net profits                       8,368,905      13,018,055      32,824,629      49,513,035
                                -----------     -----------     -----------     -----------

Net overriding royalty
   interest                              75%             75%             75%             75%
                                -----------     -----------     -----------     -----------

Royalty income                  $ 6,276,679     $ 9,763,541     $24,618,472     $37,134,776
                                ===========     ===========     ===========     ===========
</TABLE>

ITEM 3. QUALITATIVE AND QUANTITATIVE DISCLOSURES ABOUT MARKET RISK

Not applicable.


                                      -12-
<PAGE>   13



                           PART II - OTHER INFORMATION

Item 1.         Legal Proceedings

                The Trust is not a party to any litigation. However, the Trust
                is aware that BROG is involved in litigation from time to time
                that could affect the royalty income received by the Trust.

                A lawsuit has been commenced against BROG by certain royalty and
                overriding royalty owners on behalf of those persons similarly
                situated. The suit involves properties that are burdened by the
                Trust's royalty interest. This case is one of six virtually
                identical class actions filed against New Mexico gas producers.
                All such cases have been consolidated in the First Judicial
                District of Santa Fe County, New Mexico in a case filed
                September 1, 1995 and styled San Juan 1990-A, L.P., et al. v. El
                Paso Production Company and Meridian Oil Inc. The plaintiffs
                allege that they and members of the proposed class have been
                underpaid for royalties and overriding royalties. The plaintiffs
                have sought to certify the actions as class actions and seek
                monetary damages. The court has denied class certification.
                Because of the pending nature of the litigation, exposure to the
                Trust from this suit cannot be quantified. However, if the
                plaintiffs who have interests in properties that are burdened by
                the Trust are successful, royalty income received by the Trust
                could decrease.

                In addition, the Trust is aware of an administrative claim
                initiated by the Mineral Management Service of the United States
                Department of the Interior (the "MMS") against BROG by demand
                letter dated March 17, 1997 regarding a gas contract settlement
                dated March 1, 1990, between BROG and certain other parties
                thereto. The claim alleges that additional royalties are due on
                production from federal and Indian leases in the State of New
                Mexico on properties that are burdened by the Royalty. BROG
                filed its statement of reasons in June 1997 thereby contesting
                whether the royalties are payable as claimed. If the MMS claim
                is successful, royalty income received by the Trust could
                decrease.

Items 2-5       Not Applicable

Item 6.         Exhibits and Reports on Form 8-K

                (a)  Exhibits

                     (4)(a)  San Juan Basin Royalty Trust Indenture dated
                             November 3, 1980, between Southland Royalty Company
                             (now Burlington Resources Oil & Gas Company) and
                             The Fort Worth National Bank (now Bank One, Texas,
                             N.A.), as Trustee, heretofore filed as Exhibit
                             (4)(a) to the Trust's Annual Report on Form 10-K to
                             the Securities and Exchange Commission for the
                             fiscal year ended December 31, 1980 is incorporated
                             herein by reference.

                     (4)(b)  Net Overriding Royalty Conveyance from Southland
                             Royalty Company (now Burlington Resources Oil & Gas
                             Company) to The Fort Worth National Bank (now Bank
                             One, Texas, N.A.), as Trustee, dated November 3,
                             1980 (without Schedules), heretofore filed as
                             Exhibit (4)(b) to the Trust's Annual Report on Form
                             10-K to the Securities and Exchange Commission for
                             the fiscal year ended December 31, 1980 is
                             incorporated herein by reference.

                     (27)    Financial Data Schedule

                (b)  Reports on Form 8-K

                     No reports on Form 8-K were filed during the quarter ended
September 30, 1998.


                                      -13-
<PAGE>   14



                                   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.

                                     BANK ONE, TEXAS, N.A., AS TRUSTEE FOR THE
                                     SAN JUAN BASIN ROYALTY TRUST


                                             By /s/ LEE ANN ANDERSON
                                                -------------------------------
                                                     Lee Ann Anderson
                                                      Vice President

Date:  November 14, 1998


               (The Trust has no directors or executive officers.)

                                      -14-
<PAGE>   15


                                INDEX TO EXHIBITS


    EXHIBIT
    NUMBER                           EXHIBIT

    (4)(a)     San Juan Basin Royalty Trust Indenture dated November 3, 1980,
               between Southland Royalty Company (now Burlington Resources Oil &
               Gas Company) and The Fort Worth National Bank (now Bank One,
               Texas, N.A.), as Trustee, heretofore filed as Exhibit (4)(a) to
               the Trust's Annual Report on Form 10-K to the Securities and
               Exchange Commission for the fiscal year ended December 31, 1980
               is incorporated herein by reference.*


    (4)(b)     Net Overriding Royalty Conveyance from Southland Royalty Company
               (now Burlington Resources Oil & Gas Company) to The Fort Worth
               National Bank (now Bank One, Texas, N.A.), as Trustee, dated
               November 3, 1980 (without Schedules), heretofore filed as Exhibit
               (4)(b) to the Trust's Annual Report on Form 10-K to the
               Securities and Exchange Commission for the fiscal year ended
               December 31, 1980 is incorporated herein by reference.*

     (27)      Financial Data Schedule **


*    A copy of this Exhibit is available to any Unit holder, at the actual cost
     of reproduction, upon written request to the Trustee, Bank One, Texas,
     N.A., P.O. Box 2604, Fort Worth, Texas 76113.
**   Filed herewith.