<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 June 30, 1998


                           Commission File No. 1-8032



                          SAN JUAN BASIN ROYALTY TRUST


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


                     Bank One, Texas, N.A., 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 August 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 June 30,
1998, and the distributable income and changes in trust corpus for the
three-month and six-month periods ended June 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 June 30, 1998 and for
the three-month and six-month periods ended June 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 June 30, 1998 and the
related condensed statements of distributable income and changes in trust corpus
for the three-month and six-month periods ended June 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

July 25, 1998




                                      -3-
<PAGE>   4

SAN JUAN BASIN ROYALTY TRUST

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

<TABLE>
<CAPTION>
                                                                                        JUNE 30,         DECEMBER 31,
ASSETS                                                                                    1998               1997
                                                                                      (UNAUDITED)

<S>                                                                                   <C>                <C>
Cash and short-term investments                                                          $  1,918,871       $  5,111,832
Net overriding royalty interest in producing
   oil and gas properties (net of accumulated
   amortization of $79,855,904 and $77,156,080
   at June 30, 1998 and December 31, 1997, respectively)                                   53,419,624         56,119,448
                                                                                         ------------       ------------

                                                                                         $ 55,338,495       $ 61,231,280
                                                                                         ============       ============

LIABILITIES AND TRUST CORPUS

Distribution payable to Unit holders                                                     $  1,918,871       $  5,111,832
Commitments and contingencies
Trust corpus - 46,608,796 Units of beneficial
   interest authorized and outstanding                                                     53,419,624         56,119,448
                                                                                         ------------       ------------

                                                                                         $ 55,338,495       $ 61,231,280
                                                                                         ============       ============
</TABLE>



CONDENSED STATEMENTS OF DISTRIBUTABLE INCOME (UNAUDITED)
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                    THREE MONTHS ENDED                       SIX MONTHS ENDED
                                                         JUNE 30,                                JUNE 30,
                                              --------------------------------       ---------------------------------
                                                  1998              1997                  1998               1997

<S>                                            <C>               <C>                  <C>                <C>         
Royalty income                                 $ 6,678,662       $ 8,899,973          $ 18,341,793       $ 27,371,235
Interest income                                     17,154            26,888                45,202             54,545
                                               -----------       -----------          ------------       ------------

                                                 6,695,816         8,926,861            18,386,995         27,425,780

General and administrative
   expenditures                                    288,887           361,751               538,094            593,253
                                               -----------       -----------          ------------       ------------

Distributable income                           $ 6,406,929       $ 8,565,110          $ 17,848,901       $ 26,832,527
                                               ===========       ===========          ============       ============


Distributable income per Unit
   (46,608,796 Units)                          $   .137462       $   .183766          $    .382951       $    .575696
                                               ===========       ===========          ============       ============
</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                         SIX MONTHS ENDED
                                                      JUNE 30,                                  JUNE 30,
                                        -----------------------------------      ------------------------------------
                                               1998               1997                  1998               1997

<S>                                       <C>                <C>                   <C>                <C>         
Trust corpus, beginning of period         $ 54,613,230       $ 60,637,211          $ 56,119,448       $ 62,808,148
Amortization of net overriding
   royalty interest                         (1,193,606)        (1,410,107)           (2,699,824)         (3,581,044)
Distributable income                         6,406,929          8,565,110            17,848,901          26,832,527
Distributions declared                      (6,406,929)        (8,565,110)          (17,848,901)        (26,832,527)
                                          ------------       ------------          ------------        ------------

Trust corpus, end of period               $ 53,419,624       $ 59,227,104          $ 53,419,624        $ 59,227,104
                                          ============       ============          ============        ============
</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
      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



                                      -6-
<PAGE>   7

      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 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 or at 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.

The Trust is reliant on the performance of BROG and third party vendors for the
receipt of Royalty income, payment of expenses and disbursement of distributable
income. The Trust has made formal inquiries to BROG and significant third party
vendors to determine the extent to which the Trust is vulnerable to BROG and
third parties' failure to remediate their own Year 2000 issues. The Trustee can
provide no assurance as to whether BROG and third party vendors will
successfully address the Year 2000 issue. Failing to successfully address the
Year 2000 issue by BROG and third party vendors could have a material adverse
impact on the Trust and its Unit holders.

THREE MONTHS ENDED JUNE 30, 1998 AND JUNE 30, 1997:

The San Juan Basin Royalty Trust received royalty income of $6,678,662 and
interest income of $17,154 during the second quarter of 1998. After deducting
administrative expenses of $288,887 distributable income for the quarter was
$6,406,929 ($.137462 per Unit). In the second quarter of 1997, royalty income
was $8,899,973, interest income was $26,888, administrative expenses were
$361,751 and distributable income was $8,565,110 ($.183766 per Unit). The tax
credit relating to production from coal seam wells totaled approximately $.04
per Unit for both the second quarter of 1998 and the second 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 second quarter of 1998 were as follows:

<TABLE>
<S>                                           <C>      
          April                               $ .039897
          May                                   .056395
          June                                  .041170
                                              ---------

          Quarter Total                       $ .137462
                                              =========
</TABLE>




                                      -8-
<PAGE>   9
The royalty income distributed in the second quarter of 1998 was lower than that
distributed in the second quarter of 1997, primarily due to a decrease in the
average gas price from $1.75 per Mcf for the second quarter of 1997 to $1.70 per
Mcf for the second quarter of 1998 and to an increase in capital costs during
the second quarter of 1998. Interest earnings for the quarter ended June 30,
1998, as compared to the quarter ended June 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.

The capital costs attributable to the properties from which the Trust's 75% net
overriding royalty ("Royalty") was carved (the "Underlying Properties") for the
second quarter of 1998 were reported by BROG as $4,040,043 versus $1,793,762 for
the second 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
recently 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 $2,857,822 for the second quarter of 1998 as compared to
$2,767,104 for the second quarter of 1997.

BROG has informed the Trustee that during the second quarter of 1998, 5 gross
(3.36 net) conventional wells were completed on the Underlying Properties. There
was 1 gross (.04 net) coal seam and 27 gross (5.71 net) conventional wells in
progress at June 30, 1998. Six gross (4.30 net) conventional wells were
recompleted and 9 gross (.36 net) coal seam well recavitations were completed on
the Underlying Properties in the second quarter of 1998. Five gross (1.57 net)
conventional well recompletions, 5 gross (.22 net) coal seam recompletions and
12 gross (1.31 net) coal seam recavitations were in progress at June 30, 1998.
By comparison, sixteen gross (1.55 net) conventional wells were completed on the
Underlying Properties in the second quarter of 1997. There was 1 gross (.04 net)
coal seam and 18 gross (.81 net) conventional wells in progress at June 30,
1997. One gross (.87 net) conventional well recompletion and 4 gross (.16 net)
coal seam recompletions were in progress at June 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 June 30, 1998 is associated with actual gas
and oil production during February 1998 through April 1998 from the Underlying
Properties. Gas and oil sales from the Underlying Properties for the quarters
ended June 30, 1998 and 1997 were as follows:

<TABLE>
<CAPTION>
                                                                          1998            1997

<S>                                                                   <C>              <C>
Gas:
    Total sales (Mcf)                                                 10,166,912       10,213,566
    Mcf per day                                                          114,235          114,759
   Average price (per Mcf)                                                 $1.70            $1.75

Oil:
    Total sales (Bbls)                                                    24,744           27,524
    Bbls per day                                                             278              309
   Average price (per Bbl)                                                $13.22           $19.06
</TABLE>

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

<TABLE>
<S>                                                                    <C>              <C>
Gas sales (Mcf)                                                        4,287,827        5,522,845
Oil sales (Bbls)                                                          10,375           14,550
</TABLE>



                                      -9-
<PAGE>   10
During the second quarter of 1998, gas prices were lower than during the second
quarter of 1997. Gas production decreased slightly in 1998 as compared to 1997.
The price per barrel of oil during the second quarter of 1998 was $5.84 per bbl
lower than that received for the second 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.

SIX MONTHS ENDED JUNE 30, 1998 AND JUNE 30, 1997:

For the six months ended June 30, 1998 distributable income was $17,848,901
($.382951 per Unit) which was less than the $26,832,527 ($.575696 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 six
months ended June 30, 1998 was $45,202 compared to $54,545 during the first six
months of 1997. This decrease is due to a decrease in funds available for
investment. General and administrative expenses decreased to $538,094 from
$593,253 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 six months of 1998 amounted to $6,303,086. Capital
expenditures were $4,113,968 for the first six months of 1997.

Lease operating expenses and property taxes totaled $5,803,562 for the first six
months of 1998 compared to $5,654,117 for the first six months of 1997.

BROG informed the Trustee that during the six months ended June 30, 1998, 9
gross (5.09 net) conventional gas wells were completed on the Underlying
Properties. Eight gross (6.05 net) conventional wells were recompleted. Eighteen
gross (.73 net) coal seam wells were recavitated during the first six months of
1998. During the six months ended June 30, 1997, 29 gross (2.06 net)
conventional gas wells were completed on the Underlying Properties. One gross
(.84 net) coal seam and 1 gross (.83 net) conventional well were recompleted
during the first six months of 1997. Four gross (.55 net) coal seam wells were
recavitated during the first six months of 1997.



                                      -10-
<PAGE>   11
Royalty income for the six months ended June 30, 1998 is associated with actual
gas and oil production during November 1997 through April 1998 from the
Underlying Properties. Gas and oil sales from the Underlying Properties for the
six months ended June 30, 1998 and 1997 were as follows:

<TABLE>
<CAPTION>
                                                                            1998            1997

<S>                                                                       <C>              <C>
Gas:
   Total sales (Mcf)                                                      21,128,372       20,827,086
   Mcf per day                                                               116,731          115,067
   Average price (per Mcf)                                              $       1.90     $       2.41

Oil:
   Total sales (Bbls)                                                         45,216           48,486
   Bbls per day                                                                  250              268
   Average price (per Bbl)                                              $      14.53     $      20.61
</TABLE>

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

<TABLE>
<S>                                                                       <C>              <C>
Gas sales (Mcf)                                                           10,456,760       12,064,934
Oil sales (Bbls)                                                              21,935           27,213
</TABLE>

During the first six months of 1998, gas and oil prices were lower than during
the first six 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 six months ended
June 30, 1998 and 1997, respectively, was computed as shown in the following
table:

<TABLE>
<CAPTION>
                                             THREE MONTHS ENDED                      SIX MONTHS ENDED
                                                  JUNE 30,                               JUNE 30,
                                      ---------------------------------    -----------------------------------
                                          1998               1997              1998               1997

<S>                                   <C>                <C>                <C>                <C>         
Gross proceeds of sales from the
  Underlying Properties:

   Gas proceeds                       $ 17,283,052       $ 17,840,045       $ 40,077,044       $ 50,244,916
   Oil proceeds                            327,151            524,649            656,830            999,186
                                      ------------       ------------       ------------       ------------

Total                                   17,610,203         18,364,694         40,733,874         51,244,102
                                      ------------       ------------       ------------       ------------

Less production costs:
   Severance tax - Gas                   1,772,144          1,890,896          4,096,889          4,885,760
   Severance tax - Oil                      35,311             46,302             74,613             95,277
   Lease operating expenses and
      property tax                       2,857,822          2,767,104          5,803,562          5,654,117
   Capital expenditures                  4,040,043          1,793,762          6,303,086          4,113,968
                                      ------------       ------------       ------------       ------------

Total                                    8,705,320          6,498,064         16,278,150         14,749,122
                                      ------------       ------------       ------------       ------------

Net profits                              8,904,883         11,866,630         24,455,724         36,494,980
                                      ------------       ------------       ------------       ------------

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

Royalty income                        $  6,678,662       $  8,899,973       $ 18,341,793       $ 27,371,235
                                      ============       ============       ============       ============
</TABLE>




                                      -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. 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 where the case is 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
                brought by the Mineral Management Service of the United States
                Department of the Interior (the "MMS") against BROG 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. 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
                     June 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     LEE ANN ANDERSON
                                                  ------------------------------
                                                       Lee Ann Anderson
                                                        Vice President

Date: August 13, 1998


               (The Trust has no directors or executive officers.)





                                      -14-
<PAGE>   15


                                INDEX TO EXHIBITS


<TABLE>
<CAPTION>
                                                                                                  SEQUENTIALLY
               EXHIBIT                                                                              NUMBERED
               NUMBER                                EXHIBIT                                          PAGE

               <S>        <C>                                                                   <C>
               (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 **
</TABLE>


*    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.