<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, 1999


                           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 13, 1999:
46,608,796


<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,
1999, and the distributable income and changes in trust corpus for the
three-month and six-month periods ended June 30, 1999 and 1998 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, 1999 and for
the three-month and six-month periods ended June 30, 1999 and 1998 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, 1999 and the
related condensed statements of distributable income and changes in trust corpus
for the three-month and six-month periods ended June 30, 1999 and 1998. 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, 1998, 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 22, 1999, 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, 1998 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 15, 1999

                                       -3-


<PAGE>   4


SAN JUAN BASIN ROYALTY TRUST

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

<TABLE>
<CAPTION>


                                                                 JUNE 30,          DECEMBER 31,
ASSETS                                                             1999                1998
                                                               (UNAUDITED)
<S>                                                            <C>                 <C>
Cash and short-term investments                                $ 1,443,736         $ 2,665,562
Net overriding royalty interest in producing
   oil and gas properties (net of accumulated
   amortization of $84,934,900  and $82,187,508
   at June 30, 1999 and December 31, 1998, respectively)        48,340,628          51,088,020
                                                               -----------         -----------
                                                               $49,784,364         $53,753,582

LIABILITIES AND TRUST CORPUS

Distribution payable to Unit holders                           $ 1,443,736         $ 2,665,562
Commitments and contingencies
Trust corpus - 46,608,796 Units of beneficial
   interest authorized and outstanding                          48,340,628          51,088,020
                                                               -----------         -----------
                                                               $49,784,364         $53,753,582
                                                               ===========         ===========
</TABLE>



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

<TABLE>
<CAPTION>


                                         THREE MONTHS ENDED                 SIX MONTHS ENDED
                                               JUNE 30,                         JUNE 30,
                                      ---------------------------     ---------------------------
                                          1999            1998            1999          1998
<S>                                   <C>             <C>             <C>             <C>
Royalty income                        $ 5,359,825     $ 6,678,662     $12,405,031     $18,341,793
Interest income                            16,103          17,154          29,729          45,202
Other                                     892,496                         892,496
                                      -----------     -----------     -----------     -----------

                                        6,268,424       6,695,816      13,327,256      18,386,995

General and administrative
   expenditures                           324,515         288,887         591,464         538,094
                                      -----------     -----------     -----------     -----------

Distributable income                  $ 5,943,909     $ 6,406,929     $12,735,792     $17,848,901
                                      ===========     ===========     ===========     ===========

Distributable income per Unit
   (46,608,796 Units)                 $   .127528     $   .137462     $   .273249     $   .382951
                                      ===========     ===========     ===========     ===========
</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,
                                      ------------------------------      ------------------------------
                                           1999             1998              1999              1998
<S>                                   <C>               <C>               <C>               <C>
Trust corpus, beginning of period     $ 49,714,087      $ 54,613,230      $ 51,088,020      $ 56,119,448
Amortization of net overriding
   royalty interest                     (1,373,459)       (1,193,606)       (2,747,392)       (2,699,824)
Distributable income                     5,943,909         6,406,929        12,735,792        17,848,901
Distributions declared                  (5,943,909)       (6,406,929)      (12,735,792)      (17,848,901)
                                      ------------      ------------      ------------      ------------

Trust corpus, end of period           $ 48,340,628      $ 53,419,624      $ 48,340,628      $ 53,419,624
                                      ============      ============      ============      ============
</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%. The Royalty Income amount of $5,359,825 for the
          quarter ended June 30, 1999, does not include the $892,496 paid to the
          Trust for a one-time business interruption insurance claim.

      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 gas wells
      beginning in 1989. Under Section 29 of the Internal Revenue Code, coal
      seam gas production from wells drilled prior to January 1, 1993 (including
      certain wells recompleted in coal seams formations thereafter), generally
      qualifies for the federal income tax credit for producing non-conventional
      fuels if such production and the sale thereof occurs before January 1,
      2003. For 1998, this tax credit was $1.06 per MMBtu. For qualifying
      production of the Trust, each Unit holder must determine his pro rata
      share of such production based


                                       -6-


<PAGE>   7


      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 summary Section 29 tax credit information related
      to Trust Properties by BROG, which information is then passed along to the
      Unit holders. In Nielson-True Partnership, et al, v. Commissioner, a 1997
      Tax Court decision, the court ruled that nonconventional fuel (such as
      coal seam gas) produced from a well drilled and completed in an otherwise
      qualifying formation prior to December 31, 1992, is not eligible for the
      Section 29 credit unless the producer has received an appropriate well
      category determination from the Federal Energy Regulatory Commission
      ("FERC"). On March 23, 1999, the U. S. Court of Appeals for the 10th
      Circuit affirmed that decision. Dictum in the appeals court's decision
      (which is not binding as precedent) even suggests that, contrary to the
      clear implications of a 1993 Internal Revenue Service ruling, lack of such
      a well category determination may render the Section 29 credit unavailable
      in respect of production from wells recompleted in a qualified formation
      after January 1, 1993, the date that FERC's authority to render well
      category determinations ended (so that obtaining the requisite
      determination for any such well was impossible). Many producers assert
      that wells meeting the definitional requirements applied by FERC in
      rendering well category determinations are eligible for the Section 29
      credit regardless of whether a well category determination is actually
      applied for or received, particularly for wells recompleted in qualifying
      formations after January 1, 1993, and additional litigation (and perhaps a
      legislative initiative) on this issue is to be expected.

      In some cases the extent to which production from the various coal seam
      gas wells in which the Trust holds an interest would qualify for the
      Section 29 credit under the standards applied in the Nielson-True case is
      unclear, and the Trustee has requested that BROG provide clarification and
      an assessment of the effects of the foregoing, if any, on the Trust and
      its Unit holders. Pending such clarification and assessment, or further
      developments, or both, however, the availability of Section 29 credits to
      Unit holders in respect of some portion of the Trust's coal seam gas
      production could be subject to debate and challenge.

      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 January 1, 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 Trustee has adopted an extensive and comprehensive testing plan to
help ensure that its systems will function properly before, during and after the
year 2000. The Trust has made formal inquiries of BROG and significant third
party vendors, including Harris Trust and Savings Bank, the transfer agent for
the Trust, to determine the extent to which the Trust is vulnerable to failure
by BROG or such other third parties to remediate their own Year 2000 issues.

The Trust is aware that BROG has assessed its information technology for Year
2000 issues. BROG's Year 2000 readiness plan involves four phases: assessment,
remediation, testing and implementation. BROG has completed all four phases for
all of its significant information technology. BROG has reported that while its
assessment confirmed that information technology exposures were not material,
assets used in producing, gathering and transporting hydrocarbons were
determined to be at risk of encountering Year 2000 problems. BROG further
reports that it has completed the remediation, testing and implementation phases
for such operating equipment with the goal of ensuring that all critical
operating equipment under its control remains operational. BROG has contacted
all of its third-party vendors that it considers material to its operations. All
such vendors have responded that they believe that Year 2000 issues will not
have a material adverse effect on their operations. BROG has surveyed the
operators of its three primary gathering and pipeline systems in the San Juan
Basin, including the operators that transport the gas gathered from the
Underlying Properties. BROG and other major producers in the San Juan Basin have
developed contingency plans to deal with unforeseen failures to information
technology with respect to these gathering and pipeline systems.

The Trust 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. 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.


                                       -8-



<PAGE>   9


THREE MONTHS ENDED JUNE 30, 1999 AND JUNE 30, 1998:

The Trust received royalty income of $5,359,825 and interest income of $16,103
during the second quarter of 1999. The Royalty Income amount of $5,359,825 for
the quarter ended June 30, 1999, does not include the $892,496 paid to the Trust
for a one-time business interruption insurance claim. After deducting
administrative expenses of $324,515 distributable income for the quarter was
$5,943,909 ($.127528 per Unit). In the second quarter of 1998, royalty income
was $6,678,662, interest income was $17,154, administrative expenses were
$288,887 and distributable income was $6,406,929 ($.137462 per Unit). The tax
credit relating to production from coal seam wells totaled approximately $.03
per Unit for the second quarter of 1999 and $.04 per Unit for the second quarter
of 1998. For further information concerning this tax credit, Unit holders should
refer to the Trust's Annual Report for 1998. Based on 46,608,796 Units
outstanding, the per Unit distributions during the second quarter of 1999 were
as follows:

<TABLE>
<CAPTION>

<S>                      <C>
April                    $.060846
May                       .035706
June                      .030976
                         --------
Quarter Total            $.127528
                         ========
</TABLE>


The royalty income distributed in the second quarter of 1999 was lower than that
distributed in the second quarter of 1998, primarily due to a decrease in the
average gas price from $1.70 per Mcf for the second quarter of 1998 to $1.34 per
Mcf for the second quarter of 1999, partially offset by a decrease in capital
costs during the second quarter of 1999. Interest earnings for the quarter ended
June 30, 1999, as compared to the quarter ended June 30, 1998, were lower,
primarily due to decreased funds available for investment. Administrative
expenses were higher 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 1999 were reported by BROG as $2,687,005 versus $4,040,043 for
the second quarter of 1998. BROG indicates that the majority of the decrease in
capital expenditures is attributable to the timing of payment of invoices
related to the 1999 infill program and a greater cost bearing interest
associated with 1998 capital workovers compared to 1999. Lease operating
expenses and property taxes increased to $3,159,960 for the second quarter of
1999 as compared to $2,857,822 for the second quarter of 1998 due to the first
delivery of infill wells from the 1998 capital program.

BROG has informed the Trustee that during the second quarter of 1999, 17 gross
(.30 net) conventional wells were completed on the Underlying Properties. There
were 66 gross (14.28 net) conventional wells and eight gross (1.45 net)
recompletions in progress at June 30, 1999. Seven gross (.048 net) coal seam
recavitations were completed and 14 gross (.27 net) coal seam recavitations were
in progress in the second quarter of 1999. Three gross (1.42 net) coal seam
wells and one gross (.108 net) coal seam recompletion were in progress at June
30, 1999. By comparison, five gross (3.36 net) conventional wells were completed
on the Underlying Properties during the second quarter of 1998. There was one
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
nine 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, five gross (.22 net) coal seam recompletions
and 12 gross (1.31 net) coal seam recavitations were in progress at June 30,
1998.


                                       -9-


<PAGE>   10


Royalty income for the quarter ended June 30, 1999 is associated with actual gas
and oil production during February 1999 through April 1999 from the Underlying
Properties. Gas and oil sales from the Underlying Properties for the quarters
ended June 30, 1999 and 1998 were as follows:

<TABLE>
<CAPTION>

                                      1999            1998

<S>                                <C>            <C>
Gas:
    Total sales (Mcf)              10,533,677     10,166,912
    Mcf per day                       118,356        114,235
   Average price (per Mcf)         $     1.34     $     1.70

Oil:
    Total sales (Bbls)                 18,074         24,744
    Bbls per day                          203            278
   Average price (per Bbl)         $    12.65     $    13.22
</TABLE>

Gas and oil sales attributable to the Royalty for the quarters ended June 30,
1999 and 1998 were as follows:

<TABLE>
<CAPTION>

                                      1999            1998

<S>                                 <C>            <C>
Gas sales (Mcf)                     4,393,718      4,287,827
Oil sales (Bbls)                        7,598         10,375
</TABLE>

During the second quarter of 1999, gas prices were lower than during the second
quarter of 1998. Gas production increased slightly in 1999 as compared to 1998.
The price per barrel of oil during the second quarter of 1999 was $.57 per bbl
lower than that received for the second quarter of 1998 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. BROG has distributed
requests for proposals to 19 gas marketing firms as part of the process of
putting a successor contract in place for marketing the Trust gas commencing
January 1, 2000. Unit holders are referred to Note 6 of the Notes to Financial
Statements in the Trust's 1998 Annual Report for further information concerning
the marketing of gas produced from the Underlying Properties.

SIX MONTHS ENDED JUNE 30, 1999 AND 1998:

For the six months ended June 30, 1999 distributable income was $12,735,792
($.273249 per Unit) which was less than the $17,848,901 ($.382951 per Unit) of
income distributed during the same period in 1998. The decrease resulted
primarily from decreases in gas and oil prices, partially offset by the one-time
insurance proceeds. Interest income for the six months ended June 30, 1999 was
$29,729 compared to $45,202 during the first six months of 1998. This decrease
is due to a decrease in funds available for


                                      -10-

<PAGE>   11


investment. General and administrative expenses increased to $591,464 from
$538,094 during the 1998 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 1999 amounted to $4,960,206. Capital
expenditures were $6,303,086 for the first six months of 1998. Lease operating
expenses and property taxes totaled $5,955,762 for the first six months of 1999
compared to $5,803,562 for the first six months of 1998.

BROG advised the Trustee that during the six months ended June 30, 1999, 22
gross (.401 net) conventional wells were completed on the Underlying
Properties. One gross (.65 net) conventional well was completed. Twelve gross
(.144 net) coal seam wells were recavitated during the first six months of 1999.
During the six months ended June 30, 1998, nine 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.

Royalty income for the six months ended June 30, 1999 is associated with actual
gas and oil production during November 1998 through April 1999 from the
Underlying Properties. Gas and oil sales from the Underlying Properties for the
six months ended June 30, 1999 and 1998 were as follows:

<TABLE>
<CAPTION>

                                                     1999           1998
<S>                                               <C>            <C>
Gas:
   Total sales (Mcf)                              20,871,116     21,128,372
   Mcf per day                                       115,310        116,731
   Average price (per Mcf)                       $      1.44    $      1.90

Oil:
   Total sales (Bbls)                                 36,520         45,216
   Bbls per day                                          202            250
   Average price (per Bbl)                       $     11.12    $     14.53
</TABLE>


Gas and oil sales attributable to the Royalty for the six months ended June 30,
1999 and 1998 were as follows:

<TABLE>
<CAPTION>

                                                     1999            1998
<S>                                                <C>           <C>
Gas sales (Mcf)                                    9,436,600     10,456,760
Oil sales (Bbls)                                      16,616         21,935
</TABLE>


During the first six months of 1999, gas and oil prices were lower than during
the first six months of 1998. 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, 1999 and 1998, respectively, was computed as shown in the following
table:


<TABLE>
<CAPTION>

                                                  THREE MONTHS ENDED                        SIX MONTHS ENDED
                                                       JUNE 30,                                 JUNE 30,
                                         --------------------------------------  ------------------------------
                                                1999               1998              1999              1998
<S>                                        <C>                <C>                <C>               <C>
Gross proceeds of sales from the
   Underlying Properties:

   Gas proceeds                            $ 14,138,802       $ 17,283,052       $ 30,090,028      $ 40,077,044
   Oil proceeds                                 228,556            327,151            406,116           656,830
                                           ------------       ------------       ------------      ------------

Total                                        14,367,358         17,610,203         30,496,144        40,733,874
                                           ------------       ------------       ------------      ------------

Less production costs:
   Severance tax - Gas                        1,448,732          1,772,144          3,097,060         4,096,889
   Severance tax - Oil                           20,674             35,311             38,522            74,613
   Lease operating expenses and
      property tax                            2,849,124          2,857,822          5,644,926         5,803,562
   Capital expenditures                       2,997,840          4,040,043          5,271,041         6,303,086
   Other                                        (95,445)                              (95,445)
                                           ------------       ------------       ------------      ------------

Total                                         7,220,925          8,705,320         13,956,104        16,278,150
                                           ------------       ------------       ------------      ------------

Net profits                                   7,146,433          8,904,883         16,540,040        24,455,724
                                           ------------       ------------       ------------      ------------

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

Royalty income                             $  5,359,825       $  6,678,662       $ 12,405,031      $ 18,341,793
                                           ============       ============       ============      ============
</TABLE>

ITEM 3.    QUALITATIVE AND QUANTITATIVE DISCLOSURES ABOUT MARKET RISK

The Trust has not entered into derivative financial instruments, derivative
commodity instruments or other similar instruments during the quarter ended June
30, 1999. The Trust does not market the Trust gas, oil and/or natural gas
liquids. BROG is responsible for such marketing.



                                      -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, but the plaintiffs have renewed their request for
                class certification. Discovery in this matter is said to be near
                conclusion, and BROG anticipates summary judgement proceedings
                to occur in the fall of 1999. 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. BROG filed its statement of reasons in June 1997
                thereby contesting whether the royalties are payable as claimed.
                BROG has informed the Trust that the administrative claim is in
                the appeal process. If the MMS claim is successful, royalty
                income received by the Trust could decrease.

                BROG is in negotiations with the State of New Mexico for a tax
                refund based upon a claim for reimbursement of compression costs
                used in calculating wellhead values. BROG has obtained the
                approval of the Attorney General of New Mexico of a settlement
                in the amount of $4,200,000, but no payment has yet been
                received. BROG has not informed the Trust of the proportion of
                the settlement proceeds, which will be attributable to the
                Trust.

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


                                      -13-


<PAGE>   14



                             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, 1999.



                                      -14-


<PAGE>   15


                                   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:  August 13, 1999


               (The Trust has no directors or executive officers.)


                                      -15-




<PAGE>   16



                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>


  EXHIBIT
  NUMBER              EXHIBIT
  -------             -------
<S>          <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.