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

                                   Form 10-Q

             [X]  Quarterly Report Pursuant to Section 13 or 15(d)
                     of the Securities Exchange Act of 1934
               For the quarterly period ended September 30, 1998
                                              ------------------

                                       or

             [ ]  Transition Report Pursuant to Section 13 or 15(d)
                     of the Securities Exchange Act of 1934
               For the transition period from         to        
                                              -------    -------

                        Commission File Number: 1-11608

                      WILLIAMS COAL SEAM GAS ROYALTY TRUST
             (Exact name of registrant as specified in its charter)


        Delaware                                                 75-6437433
(State or other jurisdiction                                   (I.R.S. Employer
     of incorporation or                                     Identification No.)
        organization)

                                 Trust Division
                               NationsBank, N.A.
                               NationsBank Plaza
                                901 Main Street
                                   12th Floor
                              Dallas, Texas  75202
                    (Address of principal executive offices)
                                   (Zip code)

                                 (214) 508-2364
              (Registrant's telephone number, including area code)

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

         Number of units of beneficial interest outstanding at October 30,
1998: 9,700,000.
<PAGE>   2
                         PART I - FINANCIAL INFORMATION

Item 1.  Financial Statements.

         The financial statements included herein have been prepared by
NationsBank, N.A., (as successor to NationsBank of Texas, N.A.) as Trustee (the
"Trustee") of Williams Coal Seam Gas Royalty Trust (the "Trust"), 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 notes included in the Trust's Annual Report on Form 10-K for the
year ended December 31, 1997.  The December 31, 1997 balance sheet is derived
from the audited balance sheet of that date.  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 Trust as of
September 30, 1998, the distributable income for the three-month and nine-month
periods ended September 30, 1998 and 1997, and the changes in trust corpus for
the 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.

         The financial statements as of September 30, 1998 and for the
three-month and nine-month periods ended September 30, 1998 and 1997 included
herein have been reviewed by Ernst & Young LLP, independent public accountants,
as stated in their report appearing herein.





                                       2
<PAGE>   3
                     Independent Accountants' Review Report

NationsBank, N.A.,
         as Trustee of Williams Coal Seam Gas Royalty Trust

We have reviewed the accompanying condensed statement of assets, liabilities
and trust corpus of the Williams Coal Seam Gas Royalty Trust as of September
30, 1998, and the related condensed statements of distributable income for the
three- month and nine-month periods ended September 30, 1998 and 1997 and the
statements of changes in trust corpus for the 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, which will be
performed for the full year with the objective of expressing an opinion
regarding the financial statements taken as a whole.  Accordingly, we do not
express such an opinion.

As described in Note 2 to the financial statements, these financial statements
have been prepared on a modified cash basis of accounting, which is a
comprehensive basis of accounting other than generally accepted accounting
principles.

Based on our reviews, we are not aware of any material modifications that
should be made to the accompanying condensed financial statements referred to
above for them to be in conformity with the basis of accounting described in
Note 2.

We have previously audited, in accordance with generally accepted auditing
standards, the statement of assets, liabilities and trust corpus of the
Williams Coal Seam Gas 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 27, 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.


                                                               Ernst & Young LLP



Tulsa, Oklahoma
November 11, 1998





                                       3
<PAGE>   4
WILLIAMS COAL SEAM GAS ROYALTY TRUST

CONDENSED STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS 
(UNAUDITED)
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                          September 30,                       December 31,
ASSETS                                                        1998                                 1997      
                                                          -------------                       ------------   
<S>                                                   <C>                                   <C>
Current Assets -
       cash and cash equivalents                          $      79,010                       $     30,636
Royalty interests in oil
       and gas properties
       (less accumulated
       amortization of
       $86,093,750 at
       September 30, 1998
       and $77,150,886 at
       December 31, 1997)                                    52,472,913                         61,415,777
                                                          -------------                       ------------   

TOTAL ASSETS                                              $  52,551,923                       $ 61,446,413
                                                          =============                       ============  


LIABILITIES AND TRUST CORPUS
----------------------------

Current Liabilities -
       trust expenses payable                             $     141,893                       $       174,713

Trust corpus -
       9,700,000 units of
       beneficial interest
       authorized and
       outstanding                                           52,410,030                            61,271,700
                                                          -------------                       ---------------

TOTAL LIABILITIES
       AND TRUST CORPUS                                   $  52,551,923                       $    61,446,413
                                                          =============                       ===============

</TABLE>


The accompanying notes are an integral part of these financial statements.  See
accountants' review report.





                                       4
<PAGE>   5
WILLIAMS COAL SEAM GAS ROYALTY TRUST

CONDENSED STATEMENTS OF DISTRIBUTABLE INCOME (UNAUDITED)
--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                           THREE MONTHS                    THREE MONTHS
                                                              ENDED                           ENDED
                                                        September 30, 1998              September 30, 1997  
                                                        -------------------             ------------------  
<S>                                                     <C>                              <C>
Royalty income                                          $         4,761,508             $        4,707,784
Interest income                                                      15,577                         17,520
                                                        -------------------             ------------------
                                                                  4,777,085                      4,725,304

General and administrative
       expenses                                                     (88,972)                       (73,372)
                                                        -------------------              ----------------- 
Distributable income                                    $         4,688,113              $       4,651,932
                                                        ===================              -----------------

Distributable income
       per unit
       (9,700,000 units)                                $               .48              $             .48
                                                        ===================              =================

</TABLE>

The accompanying notes are an integral part of these financial statements.  See
accountants' review report.



--------------------------------------------------------------------------------



                                       5
<PAGE>   6
WILLIAMS COAL SEAM GAS ROYALTY TRUST

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

<TABLE>
<CAPTION>
                                                           NINE MONTHS                     NINE MONTHS
                                                              ENDED                           ENDED
                                                        September 30, 1998              September 30, 1997  
                                                        ------------------              ------------------  
<S>                                                     <C>                              <C>
Royalty income                                          $       13,221,630              $       14,886,953
Interest income                                                     45,378                          53,405
                                                        ------------------              ------------------  
                                                                13,267,008                      14,940,358

General and administrative
       expenses                                                   (478,807)                       (491,583)
                                                        ------------------              ------------------  
Distributable income                                    $       12,288,201              $       14,448,775
                                                        ==================              ==================

Distributable income
       per unit
       (9,700,000 units)                                $             1.31              $             1.49
                                                        ------------------              ------------------  

</TABLE>

The accompanying notes are an integral part of these financial statements.  See
accountants' review report.

--------------------------------------------------------------------------------




                                       6
<PAGE>   7
WILLIAMS COAL SEAM GAS ROYALTY TRUST

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

<TABLE>
<CAPTION>
                                                           NINE MONTHS                     NINE MONTHS
                                                              ENDED                           ENDED
                                                        September 30, 1998              September 30, 1997  
                                                        ------------------              ------------------  
<S>                                                     <C>                              <C>
Trust corpus,                                           $       61,271,700              $       70,021,573
       beginning of period
Amortization of royalty
       interests                                                (8,942,864)                     (6,544,150)
Distributable income                                            12,788,201                      14,448,775
Distributions to unitholders                                   (12,707,007)                    (14,540,358)
                                                        ------------------              ------------------  
Trust corpus, end
       of period                                        $       52,410,030              $       63,385,840
                                                        ==================              ==================

Distributions per unit
       (9,700,000 units)                                $             1.31              $             1.50
                                                        ==================              ==================

</TABLE>

The accompanying notes are an integral part of these financial statements.  See
accountants' review report.


--------------------------------------------------------------------------------




                                       7
<PAGE>   8
WILLIAMS COAL SEAM GAS ROYALTY TRUST

NOTES TO FINANCIAL STATEMENTS (UNAUDITED)

--------------------------------------------------------------------------------

1.     TRUST ORGANIZATION AND PROVISIONS

       Williams Coal Seam Gas Royalty Trust (the "Trust") was formed as a
Delaware business trust pursuant to the terms of the Trust Agreement of
Williams Coal Seam Gas Royalty Trust (as amended, the "Trust Agreement")
entered into effective as of December 1, 1992 by and among Williams Production
Company, a Delaware corporation ("WPC"), as trustor, The Williams Companies,
Inc., a Delaware corporation ("Williams"), and Nations Bank, N.A. (as successor
to NationsBank of Texas, N.A.), a national banking association (the "Trustee"),
and Chemical Bank Delaware, a Delaware banking corporation (the "Delaware
Trustee"), as trustees.  The trustees are independent financial institutions.

       The Trust was formed to acquire and hold certain net profits interests
(the "Royalty Interests") in proved natural gas properties located in the San
Juan Basin of New Mexico and Colorado (the "Underlying Properties") owned by
WPC.  The Trust was initially created effective as of December 1, 1992 with a
$100 contribution by WPC.  On January 21, 1993, the Royalty Interests were
conveyed to the Trust by WPC pursuant to the Net Profits Conveyance (the
"Conveyance") dated effective as of October 1, 1992 by and among WPC, Williams,
the Trustee and the Delaware Trustee, in consideration for all the 9,700,000
authorized units of beneficial interest in the Trust ("Units").  WPC
transferred its Units by dividend to its parent, Williams, which sold an
aggregate of 5,980,000 Units to the public through various underwriters in
January and February 1993 (the "Public Offering").  During the second quarter
of 1995 Williams transferred its Units to Williams Holdings of Delaware, Inc.
(WHD), a separate holding company for Williams' non regulated businesses.
Substantially all of the production attributable to the Underlying Properties
is from the Fruitland coal formation and constitutes "coal seam" gas that
entitles the owners of such production, provided certain requirements are met,
to tax credits for Federal income tax purposes pursuant to Section 29 of the
Internal Revenue Code of 1986, as amended.

       On May 7, 1997, effective as of May 1, 1997, WPC transferred the
Underlying Properties to an unaffiliated third party ("Buyer") pursuant to the
terms of the Purchase and Sale Agreement dated as of May 1, 1997 (herein so
called) between WPC and Buyer (the "Transaction").  Prior to the Transaction,
WPC had owned the Underlying Properties, subject to and burdened by the Royalty
Interests owned by the Trust, since the inception of the Trust.  Neither the
Trustee nor the Delaware Trustee has any control over or responsibility
relating to the operation of the Underlying Properties.  The Transaction was
previously reported in its Form 10-Q for the quarter ended March 31, 1997, and
thereafter described in more detail in the Current Report on Form 8-K filed
with the Securities and Exchange Commission on June 23, 1997 (the "Transaction
Form 8-K").

       Concurrently with the Transaction, WPC and Buyer entered into a
Management Services Agreement dated May 1, 1997 (the "Management Services
Agreement") whereby WPC agreed, among other things, to continue to manage and
operate the Underlying Properties and to handle the receipt and payment of
funds with respect thereto.  Prior to the Transaction, WPC received all





                                       8
<PAGE>   9
payments relating to the Underlying Properties and, pursuant to the Conveyance,
paid to the Trust the portion thereof attributable to the Royalty Interests.
Following the Transaction, under the Management Services Agreement, WPC
continues to collect all revenues on behalf of Buyer and remains obligated to
pay to the Trust on behalf of Buyer the amounts payable with respect to the
Royalty Interests.

       Concurrently with the Transaction, WPC, Williams, the Trust and Buyer
entered into an Agreement dated May 7, 1997 (the "Supplemental Agreement")
pursuant to which (i) the parties acknowledged that WPC was selling the
Underlying Properties to Buyer, but retaining all of its duties and obligations
under the Trust Agreement, Conveyance and related documents (the "Trust
Documents"), subject to the terms and conditions set forth in the Purchase and
Sale Agreement and the agreements entered into pursuant to the Purchase and
Sale Agreement, (ii) Williams and WPC each confirmed and agreed that,
notwithstanding the sale of the Underlying Properties to Buyer, Williams and
WPC would continue to perform their respective obligations to the Trust
pursuant to the Trust Documents, including without limitation the performance
assurances of Williams set forth in the Conveyance, and (iii) Buyer
acknowledged and agreed that it was purchasing the Underlying Properties
burdened by the Royalty Interests owned by the Trust.

       As a result of these assurances and the Trustee's belief that the
Transaction will have no adverse effect on Unitholders, the information and
descriptions set forth herein give no effect to the Transaction.  Consequently,
with regard to ownership of the Underlying Properties, references herein to
"WPC" with respect to those periods after the effective date of the Transaction
are to Buyer.  The Transaction Form 8-K should be consulted for further
information on the Transaction.

       The Trustee has the power to collect and distribute the proceeds
received by the Trust and to pay Trust liabilities and expenses.  The Delaware
Trustee has only such powers as are set forth in the Trust Agreement and is not
empowered to otherwise manage or take part in the business of the Trust.  The
Royalty Interests are passive in nature and neither the Delaware Trustee nor
the Trustee has any control over or any responsibility relating to the
operation of the Underlying Properties.

       The Trust will terminate no later than December 31, 2012, subject to
earlier termination under certain circumstances described in the Trust
Agreement (the "Termination Date").  Cancellation of the Trust will occur on or
following the Termination Date when all Trust assets have been sold and the net
proceeds thereof distributed to Unitholders.

       The only assets of the Trust, other than cash and cash equivalents being
held for the payment of expenses and liabilities and for distribution to
Unitholders, are the Royalty Interests.  The Royalty Interests consist
primarily of a net profits interest (the "NPI") in the Underlying Properties.
The NPI generally entitles the Trust to receive 81 percent of the NPI Net
Proceeds, as defined below, attributable to (i) gas produced and sold from
WPC's net revenue interests (working interests less lease burdens) in the
properties in which WPC has a working interest (the "WI Properties") and (ii)
the revenue stream received by WPC attributable to its 35 percent net profits
interest in 5,348 gross acres in La Plata County, Colorado (the "Farmout
Properties").  The Royalty Interests also include a 20 percent interest in
WPC's Infill Net Proceeds, as defined below, from the sale of production if
well spacing rules are effectively modified and additional wells are drilled on
producing drilling blocks on the WI Properties (the "Infill Wells") during the
term of the Trust.  No Infill Wells have





                                       9
<PAGE>   10
been drilled on the WI Properties to date.  "NPI Net Proceeds" consists
generally of the revenue stream received by WPC from its 35 percent net profits
interest in the Farmout Properties, plus the aggregate proceeds attributable to
WPC's net revenue interest, based on the price paid at or in the vicinity of
the wellhead (the "Wellhead"), of gas produced from the WI Properties, less
WPC's share of certain taxes and costs.  "Infill Net Proceeds" consists
generally of the aggregate proceeds, based on the price at the Wellhead, of gas
produced from WPC's net revenue interest in any Infill Wells less certain taxes
and costs.  The NPI percentage is subject to certain future downward
adjustments based on a rate of return computation once cumulative aggregate
production targets are met.  The complete definitions of NPI Net Proceeds and
Infill Net Proceeds are set forth in the Conveyance.

2.     BASIS OF ACCOUNTING

       The financial statements of the Trust are prepared on a modified cash
basis and are not intended to present financial position and results of
operations in conformity with generally accepted accounting principles
("GAAP").  Preparation of the Trust's financial statements on such basis
includes the following:

       Revenues are recognized in the period in which amounts are received by
       the Trust.  General and administrative expenses are recognized on an
       accrual basis.

       Amortization of the Royalty Interests is calculated on a
       unit-of-production basis and charged directly to trust corpus.

       Distributions to Unitholders are recorded when declared by the Trustee
       (see Note 4).

       The financial statements of the Trust differ from financial statements
prepared in accordance with GAAP because royalty income is not accrued in the
period of production and amortization of the Royalty Interests is not charged
against operating results.

       Williams sold an aggregate of 5,980,000 Units of the Trust's authorized
9,700,000 Units in the Public Offering at the offering price of $20 per Unit,
retaining 3,720,000 Units.  Subsequently, Williams sold an additional 151,209
Units for $23.50 per Unit.  Accordingly, the condensed statements of assets,
liabilities and trust corpus reflect the sale of these Units at the respective
sale prices thereof, as well as the remaining 3,568,791 Units at Williams'
historical cost.  During the second quarter of 1995 Williams transferred its
Units to WHD, a separate holding company for Williams' non regulated
businesses.  If WHD, in the future, should sell all or a portion of its
retained Units, at that time, the carrying value on the Trust's statements of
assets, liabilities and trust corpus may again be adjusted from WHD's
historical cost to the subsequent sale price with respect to the Units sold.

3.     FEDERAL INCOME TAXES

       The Trust is a grantor trust for Federal income tax purposes.  As a
grantor trust, the Trust will not be required to pay Federal or state income
taxes.  Accordingly, no provision for income taxes has been made in these
financial statements.





                                       10
<PAGE>   11
       Because the Trust will be treated as a grantor trust, and because a
Unitholder will be treated as directly owning an interest in the Royalty
Interests, each Unitholder will be taxed directly on his per Unit pro rata
share of income attributable to the Royalty Interests consistent with the
Unitholder's method of accounting and without regard to the taxable year or
accounting method employed by the Trust.

       Production from coal seam gas wells drilled after December 31, 1979 and
prior to January 1, 1993, qualifies for the Federal income tax credit for
producing nonconventional fuels under Section 29 of the Internal Revenue Code.
This tax credit is calculated annually based on each year's qualified
production through the year 2002.  Such credit, based on the Unitholder's pro
rata share of qualifying production, may not reduce his regular tax liability
(after the foreign tax credit and certain other non-refundable credits) below
his alternative minimum tax.  Any part of the Section 29 credit not allowed for
the tax year solely because of this limitation is subject to certain carryover
provisions.  Each Unitholder should consult his tax advisor regarding Trust tax
compliance matters.

4.     DISTRIBUTIONS TO UNITHOLDERS

       The Trustee determines for each quarter the amount of cash available for
distribution to Unitholders.  Such amount (the "Quarterly Distribution Amount")
is an amount equal to the excess, if any, of the cash received by the Trust, on
or prior to the last day of the month following the end of each calendar
quarter from the Royalty Interests, plus, with certain exceptions, any other
cash receipts of the Trust during such quarter, over the liabilities of the
Trust paid during such quarter, subject to adjustments for changes made by the
Trustee during such quarter in any cash reserves established for the payment of
contingent or future obligations of the Trust.

       The Quarterly Distribution Amount for each quarter is payable to
Unitholders of record on the 45th day following the end of such calendar
quarter unless such day is not a business day in which case the record date is
the next business day thereafter.  The Trustee distributes the Quarterly
Distribution Amount within 60 days after the end of each calendar quarter to
each person who was a Unitholder of record on the associated record date,
together with interest estimated to be earned on such amount from the date of
receipt thereof by the Trustee to the payment date.

       In addition to the regular quarterly distributions, under certain
circumstances specified in the Trust Agreement (such as upon a purchase price
adjustment, if any, or pursuant to the sale of a Royalty Interest), the Trust
would make a special distribution (a "Special Distribution Amount").  A Special
Distribution Amount would be made when amounts received by the Trust under such
circumstances aggregated in excess of $9,000,000.  The record date for a
Special Distribution Amount will be the 15th day following receipt of amounts
aggregating a Special Distribution Amount by the Trust (unless such day is not
a business day in which case the record date will be the next business day
thereafter) unless such day is within 10 days of the record date for a
Quarterly Distribution Amount in which case the record date will be the date as
is established for the next Quarterly Distribution Amount.  Distribution to
Unitholders of a Special Distribution Amount will be made no later than 15 days
after the Special Distribution Amount record date.





                                       11
<PAGE>   12
5.     SUBSEQUENT EVENTS

       Subsequent to September 30, 1998, the Trust declared the following
distribution:

<TABLE>
<CAPTION>
                   Quarterly
                     Record                          Payment                    Distribution
                      Date                             Date                       per Unit  
                   ----------                       ----------                  ------------
                  <S>                              <C>                            <C>
                  November 16                      November 27                    $ .322739
</TABLE>

       The distribution per unit decreased from $.473926 for the third quarter
of 1998 to $.322739 for the fourth quarter of 1998.  The decrease in
distributions was mainly due to prior period adjustments for federal unit
acreage expansion and an increase in operating and capital costs.  The decrease
in distributions was also impacted by a negative prior period adjustment for
the Farmout Properties.  Expansions of federal unit acreage can either increase
or decrease the Trust's ownership of particular wells resulting in potential
adjustments of production for prior periods and associated distributions to
unitholders can either increase or decrease.  Federal unit acreage expansions
are determined by the commercial value of the property as valued by the
operator and approved by the U.S. Bureau of Land Management (BLM).  Williams
Production Company does not operate any wells in these federal acreage units.

6.     CONTINGENCIES

       Under the terms of the gas purchase contract entered into by WPC and WFS
Gas Resources Company ("WFS Gas Resources"), an affiliate of WPC, as amended
(the "Gas Purchase Contract"), additional revenues may be paid to the Trust to
meet the minimum gas price provision of 97 percent of $1.75 per MMBtu (the
"Minimum Purchase Price").  This additional revenue is subject to recoupment by
the purchaser from future revenues received from production commencing January
1, 1994 when the applicable index price exceeds the Minimum Purchase Price as
long as the Minimum Purchase Price commitment is in effect.  The primary term
of the Gas Purchase Contract expired on December 31, 1997, however for calendar
year 1998, WFS Gas Resources did not elect to exercise its annual option to
discontinue paying under the Gas Purchase Contract by giving notice of its
election to pay solely on an index price.  Consequently, WFS Gas Resources will
continue to purchase gas pursuant to the Gas Purchase Contract through December
31, 1998 and for additional years until such time as WFS Gas Resources
exercises its annual option to discontinue paying under the Gas Purchase
Contract.

       During the third quarter of 1998, the applicable index price was below
the Minimum Purchase Price resulting in accruals in the price credit account
established pursuant to the terms of the Gas Purchase Contract.  WPC estimates
that, as of September 30, 1998, WFS Gas Resources had aggregate price credits
in the price credit account of approximately $11.5 million of which the Trust's
81 percent interest was approximately $9.3 million.  The applicable index price
was below the Minimum Purchase Price in October 1998.

       The entitlement of WFS Gas Resources to recoup the price credits means
that if and when the applicable Blanco Hub Spot Price rises above $1.75 per
MMBtu, future royalty income paid to the Trust would be reduced until such time
as such price credits have been fully recouped.  Corresponding cash
distributions to Unitholders would also be reduced.





                                       12
<PAGE>   13
       Southern Ute Litigation.  As previously reported by the Trust in the
public offering prospectus for the Units, each of the Trust's prior Annual
Reports on Form 10-K including the Annual report on Form 10-K for the year
ending December 31, 1997 (the "1997 Annual Report") and in the Trust's Current
Report on Form 10-Q for the quarter ending June 30, 1998 (the "Quarterly
Report") as filed with the Securities and Exchange Commission, WPC is a named
defendant in a lawsuit (the "Southern Ute Litigation") brought by the Southern
Ute Indian Tribe which, among other things, contests ownership rights in
certain coal seam gas producing properties, including a portion of the Farmout
Properties in which WPC owns a net profits interest.  A portion of the revenues
received by WPC with regard to the Farmout Properties is paid to the Trust as a
component of the NPI.  The Southern Ute Litigation represents a significant
contingency which may affect the future economic performance of the Trust,
including distributions to Unitholders, due to a possible reduction or
elimination of future Trust revenues from the disputed portion of the Farmout
Properties and due to possible recoupment by WPC of that portion of the
aggregate revenues paid to the Trust attributable to the disputed portion of the
Farmout Properties in excess of a predetermined formula amount.  Such recoupment
would be effected by WPC by withholding a portion of future revenues otherwise
payable to the Trust.  Unitholders should consult the 1997 Annual Report and the
Quarterly Report for additional information regarding the Southern Ute
Litigation and the litigation's possible consequences to the Trust and
Unitholders.

7.     POSSIBLE NPI PERCENTAGE CHANGE

       The NPI generally entitles the Trust to receive 81 percent of the NPI
Net Proceeds.  However, at the point that cumulative production from the
Underlying Properties exceeds 178.5 Bcf of gas and the internal rate of return
of the "after tax cash flow per Trust Unit" (as defined in the Conveyance) is
equal to or greater than 12 percent but not more than 14 percent, the
percentage of NPI Net Proceeds payable in respect of the NPI would be reduced
to 60 percent.  If such level of production is exceeded and such internal rate
of return of the after tax cash flow per Trust Unit exceeds 14 percent, the
percentage of NPI Net Proceeds payable in respect of the NPI would be reduced
to 40 percent.  WPC has advised the Trustee that the cumulative production from
the Underlying Properties to date has been approximately 166 Bcf.  Based upon
projections by Miller and Lents, Ltd., the Trust's independent petroleum
engineers, the internal rate of return is not currently expected to be 12
percent or higher until the third quarter of 2000, although no assurance can be
made that it will not occur sooner than projected.

Item 2.        Trustee's Discussion and Analysis of Financial Condition
               and Results of Operations.

       On May 7, 1997, effective as of May 1, 1997, WPC transferred the
Underlying Properties to an unaffiliated third party ("Buyer") pursuant to the
terms of the Purchase and Sale Agreement dated as of May 1, 1997 (herein so
called) between WPC and Buyer (the "Transaction").  Prior to the





                                       13
<PAGE>   14
Transaction, WPC had owned the Underlying Properties, subject to and burdened
by the Royalty Interests owned by the Trust, since the inception of the Trust.
Neither the Trustee nor the Delaware Trustee has any control over or
responsibility relating to the operation of the Underlying Properties.  The
Transaction was previously reported as a subsequent event by the Trust in its
Form 10-Q for the quarter ended March 31, 1997, and thereafter described in
more detail in the Current Report on Form 8-K filed with the Securities and
Exchange Commission on June 23, 1997 (the "Transaction Form 8-K").

       Concurrently with the Transaction, WPC and Buyer entered into a
Management Services Agreement dated May 1, 1997 (the "Management Services
Agreement") whereby WPC agreed, among other things, to continue to manage and
operate the Underlying Properties and to handle the receipt and payment of
funds with respect thereto.  Prior to the Transaction, WPC received all
payments relating to the Underlying Properties and, pursuant to the Conveyance,
paid to the Trust the portion thereof attributable to the Royalty Interests.
Following the Transaction, under the Management Services Agreement, WPC
continues to collect all revenues on behalf of Buyer and remains obligated to
pay to the Trust on behalf of Buyer the amounts payable with respect to the
Royalty Interests.

       Concurrently with the Transaction, WPC, Williams, the Trust and Buyer
entered into an Agreement dated May 7, 1997 (the "Supplemental Agreement")
pursuant to which (i) the parties acknowledged that WPC was selling the
Underlying Properties to Buyer, but retaining all of its duties and obligations
under the Trust Agreement, Conveyance and related documents (the "Trust
Documents"), subject to the terms and conditions set forth in the Purchase and
Sale Agreement and the agreements entered into pursuant to the Purchase and
sale Agreement, (ii) Williams and WPC each confirmed and agreed that,
notwithstanding the sale of the Underlying Properties to Buyer, Williams and
WPC would continue to perform their respective obligations to the Trust
pursuant to the Trust Documents, including without limitation the performance
assurances of Williams set forth in the Conveyance, and (iii) Buyer
acknowledged and agreed that it was purchasing the Underlying Properties
burdened by the Royalty Interests owned by the Trust.

       As a result of these assurances and the Trustee's belief that the
Transaction will have no adverse effect on Unitholders, the information and
descriptions set forth herein give no effect to the Transaction.  Consequently,
with regard to ownership of the Underlying Properties, references herein to
"WPC" with respect to those periods after the effective date of the Transaction
are to Buyer.  The Transaction Form 8-K should be consulted for further
information on the Transaction.

       The Trust makes quarterly cash distributions to holders of units of
beneficial interest ("Units") in the Trust ("Unitholders").  The only assets of
the Trust, other than cash and cash equivalents being held for the payment of
expenses and liabilities and for distribution to Unitholders, are net profits
interests (the "Royalty Interests") in certain proved coal seam gas properties
located in the San Juan Basin of New Mexico and Colorado (the "Underlying
Properties").  The Royalty Interests owned by the Trust burden the Underlying
Properties, which are owned by Williams Production Company ("WPC") and not the
Trust.





                                       14
<PAGE>   15
       Distributable income of the Trust consists of the excess of royalty
income plus interest income over the general and administrative expenses of the
Trust.  Upon receipt by the Trust, royalty income is invested in short-term
investments in accordance with the Trust Agreement (as defined in Note 1 to the
financial statements of the Trust appearing elsewhere in this Form 10-Q ("Note
1")) until its subsequent distribution to Unitholders.

       The amount of distributable income of the Trust for any quarter may
differ from the amount of cash available for distribution to Unitholders in
such quarter due to differences in the treatment of the expenses of the Trust
in the determination of those amounts.  The financial statements of the Trust
are prepared on a modified cash basis pursuant to which the expenses of the
Trust are recognized when incurred.  Consequently, the reported distributable
income of the Trust for any quarter is determined by deducting from the income
received by the Trust the amount of expenses incurred by the Trust during such
quarter.  The amount of cash available for distribution to Unitholders,
however, is determined in accordance with the provisions of the Trust Agreement
and reflects the deduction from the income actually received by the Trust of
the amount of expenses actually paid by the Trust and adjustments for changes
in reserves for unpaid liabilities.  See Note 4 to the financial statements of
the Trust appearing elsewhere in this Form 10-Q for additional information
regarding the determination of the amount of cash available for distribution to
Unitholders.

Three Months and Nine Months Ended September 30, 1998 Compared to Three Months
and Nine Months Ended September 30, 1997

       For the quarter ended September 30, 1998, royalty income for the nine
month period received by the Trust amounted to $4,761,508 as compared to
$4,707,784 received for the same quarter in 1997.  For the nine months ended
September 30, 1998, royalty income received by the Trust amounted to $13,221,630
as compared to $14,886,953 received for the same period in 1997. The decrease in
royalty income for the nine month period is primarily due to adjustments in the
Federal units  and overall production decline within the Underlying Properties.
Interest income for the quarter ended September 30, 1998 was $15,577 compared to
$17,520 for the same quarter in 1997.  Interest income for the nine months ended
September 30, 1998 was $45,378 compared to $53,405 for the same period in 1997.
This decrease was primarily due to a decrease in the amount of funds available
for investment.  General and administrative expenses during the third quarter of
1998 amounted to $88,972 compared to $73,372 for the same quarter in 1997.  This
increase was primarily due to timing of payments of printing costs in the third
quarter of 1998.  General and administrative expenses during the nine months
ended September 30, 1998 amounted to $478,807 compared to $491,583 for the same
period in 1997.

       Distributable income for the quarter ended September 30, 1998 was
$4,688,113 or $.48  per Unit which is comparable to $4,651,932 or $.48 per Unit
for the third quarter of 1997.  Distributable income for the nine months ended
September 30, 1998 was $12,788,807 or $1.31 per Unit compared to $14,498,775 or
$1.49 per Unit for the same period in 1997.  This decrease was a result of the
factors stated in the preceding paragraph.  A distribution of $.473926 per Unit
was made on August 28, 1998 to Unitholders of record on August 14, 1998.

       Because the Trust incurs administrative expenses throughout a quarter
but receives its royalty income only once in a quarter, the Trustee established
in the first quarter of 1993 a cash reserve for the payment of expenses and
liabilities of the Trust.  The Trustee thereafter has adjusted the amount of
such reserve in certain quarters as required for the payment of the Trust's
expenses and liabilities,





                                       15
<PAGE>   16
in accordance with the provisions of the Trust Agreement.  The Trustee
anticipates that it will maintain for the foreseeable future a cash reserve
which will fluctuate as expenses are paid and royalty income is received.

       Royalty income to the Trust is attributable to the sale of depleting
assets.  All of the Underlying Properties burdened by the Royalty Interests
consist of producing properties.  Accordingly, the proved reserves attributable
to WPC's interest in the Underlying Properties are expected to decline
substantially during the term of the Trust and a portion of each cash
distribution made by the Trust will, therefore, be analogous to a return of
capital.  Accordingly, cash yields attributable to the Units are expected to
decline over the term of the Trust.

       Royalty income received by the Trust in a given calendar quarter will
generally reflect the sum of (i) proceeds from the sale of gas produced from
the WI Properties during the preceding calendar quarter, plus (ii) cash
received by WPC with respect to the Farmout Properties either (a) during the
preceding calendar quarter or (b) if received in sufficient time to be paid to
the Trust, in the month immediately following such calendar quarter.
Accordingly, the royalty income included in distributable income for the
quarter ended September 30, 1998 was based on production volumes and natural
gas prices for the period April through June 1998, as shown in the table below.
Due to delays associated with the receipt of income related to the Farmout
Properties, the Trust's royalty income for the 1998 third quarter reflects
estimated production volumes from the Farmout Properties for the months of
March 1998 through May 1998, as shown in the table below.  The production
volumes included in the table below are for production attributable to the
Underlying Properties, and not for production attributable to the Trust's
Royalty Interests and are net of the amount of production attributable to WPC's
royalty obligations to third parties, which is determined by contractual
arrangement with such parties.

<TABLE>
<CAPTION>
                                                      Three Months                   Three Months
                                                         Ended                             Ended
                                                     June 30, 1998                   June 30, 1997
                                                   ---------------                   -------------
<S>                                                <C>                                   <C>
Production (MMBtu) (1)
      WI Properties                                    3,946,609 (2)                     4,139,141 (4)
      Farmout Properties                               1,379,260 (3)                     1,642,399 (5)
                                                                    

Blanco Hub Spot Price
      ($/MMBtu)  (6)                              $         1.74                        $     1.83
Net Wellhead Price
      WI Properties ($/MMBtu) (6)                 $         0.93                        $     1.01
</TABLE>

---------------
(1)      Million British Thermal Units.
(2)      Includes prior period adjustments of 297,958 MMBtu.
(3)      Reflects estimated volumes for March 1998 through May 1998.  Includes
         prior period adjustments of 47,342 MMBTU.
(4)      Includes prior period adjustments of (504,768) MMBtu.
(5)      Reflects March 1997 through May 1997.





                                       16
<PAGE>   17
(6)      Simple average of estimates for the months included in the period
         presented.

         Production from the WI Properties is generally sold pursuant to a gas
purchase contract between WPC and WFS Gas Resources Company ("WFSGR") (as
successor in interest to Williams Gas Marketing Company).  The gas purchase
contract provides certain protections for WFS Gas Resources in the form of
price credits (for production purchased by WFS Gas Resources on or after
January 1, 1994) and for Unitholders when the applicable Blanco Hub Spot Price
falls below $1.75 per MMBtu and provides certain benefits for WFS Gas Resources
when the Blanco Hub Spot Price exceeds $2.00 per MMBtu.  The gas purchase
contract also provides that the price paid for gas by WFS Gas Resources is
reduced by the amount of gathering, processing and certain other costs paid by
WFS Gas Resources.

         The initial five-year term ("Primary Term") of the Gas Purchase
Contract expired on December 31, 1997.  Following the expiration of the Primary
Term, the Gas Purchase Contract will continue in effect for one or more
consecutive additional one-year terms (each such term a "Contract Year") unless
and until WFS Gas Resources exercises its annual option, exercisable fifteen
days prior to the end of each Contract Year, to discontinue purchasing gas from
WPC under the terms of the Gas Purchase Contract and instead purchase gas at a
monthly price equal to the index price of 97 percent of the Blanco Hub Spot
Price.  For the Contract Year January 1, 1998 through December 31, 1998, WFS
Gas Resources did not exercise this option and the pricing mechanism of the Gas
Purchase Contract will therefore remain in place through at least December 31,
1998.

         The Blanco Hub Spot Price was below $1.75 per MMBtu during the third
quarter of 1998. However, pursuant to the terms of the gas purchase contract,
WFS Gas Resources continued to purchase gas produced from the WI Properties at
the $1.70 minimum purchase price, less certain gathering, processing and
delivery costs paid by WFS Gas Resources, established by the gas purchase
contract; and WFS Gas Resources received a price credit from WPC for each MMBtu
of natural gas so purchased by WFS Gas Resources equal to the difference
between the $1.70 minimum purchase price and the applicable index price (which
price is equal to 97 percent of the applicable Blanco Hub Spot Price).  WPC
estimates that, as of September 30, 1998, WFS Gas Resources had aggregate price
credits of approximately $11.5 million of which the Trust's 81 percent interest
was approximately $9.3 million.  The Blanco Hub Spot Price was below $1.75 per
MMBtu in October 1998.

         The entitlement of WFS Gas Resources to recoup the price credits means
that if and when the applicable Blanco Hub Spot Price rises above $1.75 per
MMBtu, future royalty income paid to the Trust would be reduced until such time
as such price credits have been fully recouped.  Corresponding cash
distributions to Unitholders would also be reduced.

         The information in this Form 10-Q concerning production and prices
relating to the Underlying Properties is based on information prepared and
furnished by WPC to the Trustee.  The Trustee has no control over and no
responsibility relating to the operation of the Underlying Properties.





                                       17
<PAGE>   18
Year 2000

         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 Trustee has
identified its primary system that is vulnerable to the Year 2000 issue: its
General Ledger/Accounts Payable System. The Trust selected a system that has
been warranted to be Year 2000 compliant and completed the installation of the
new system at the beginning of 1998.  The cost of the system was approximately
$6,000.  To date the Trustee has incurred no other costs in connection with its
efforts to identify, assess, remediate and test the Trust's systems for Year
2000 compliance.

         The Trustee is in the process of identifying and assessing other
information technology ("IT") systems used in connection with the Trust as well
as other systems, for Year 2000 compliance.  Non-IT systems are generally more
difficult to assess because they often contain embedded technology that may be
subject to Year 2000 problems.  The total cost of the Trustee's Year 2000
efforts is expected to be approximately $10,000 (including the $6,000 referred
to above), all of which will be incurred and paid during the first two quarters
of 1998 and the first quarter of 1999.  Of this amount, the Trustee expects to
pay $4,000 for identification and assessment of affected systems.

         The Trustee has additionally identified those vendors it believes could
have an impact on its day-to-day operations if their operations were interrupted
as a result of Year 2000 problems.  The Trustee has developed a questionnaire
regarding the vendor's Year 2000 status.  These vendors, consisting primarily of
energy companies, will be contacted before January 1, 1999 to determine their
Year 2000 status. Williams Production, which provides extensive accounting
services to the Trust, has indicated that their IT Systems will be Year 2000
compliant. The Trustee is continuing discussions with Williams regarding their
certification.

         The Trustee has no reason to believe that its vendors will not be Year
2000 compliant.  In the event the Trustee learns that a vendor's system will
not be Year 2000 compliant, the Trustee will assess the potential risk and
develop contingency plans at that time.

         The Trust is a passive entity with limited business operations, and
the IT systems employed by the Trustee in connection with its duties on behalf
of the Trust are less extensive than the systems employed by many business
entities. The Trust has no formal IT budget, and the Trustee does not anticipate
making any other significant capital expenditures relating to the Trustee's IT
systems used in connection with Trust during 1998 or 1999.  Thus, the
expenditures expected to be made in connection with the Year 2000 efforts
described above will represent substantially all of the Trustee's IT-related
expenditures on behalf of the Trust during 1998 and 1999. These expenses will be
paid as expenses of the Trust.

         Because the royalty interests held by the Trust are fixed, the Trustee
is dependent upon the third parties (primarily energy companies) that hold
operating interests with respect thereto for the receipt of royalty income.
Thus, if any such third party failed to deliver royalty income, the Trustee
would have available no alternative source for such income.  The Trustee
believes that the worst case





                                       18
<PAGE>   19
scenario would be the failure by the Trustee and one or more third parties who
pay royalties to the Trust to identify or remediate Year 2000 problems on a
timely basis, which could cause the Trustee to be unable to make required
distributions to Unitholders.  Such inability could result in the incurrence by
the Trust of interest charges or other liabilities to Unitholders.   The
Trustee believes that in the event of a failure of any of its internal systems
it would be able to replace such systems in a relatively short period of time,
relying on internal resources of NationsBank, N.A., which serves as the
Trustee, although there can be no assurance that such replacement would not be
costly or that it would be completed without resulting in a significant delay
in the distributions to Unitholders.  With respect to a failure by a third
party to deliver royalty income on a timely basis, the Trustee believes that it
would have no control over the efforts of such third party to correct the
problems, and significant delays in the receipt of royalty income could result.

         The Trust will utilize both internal and external resources to achieve
Year 2000 compliance.  The Trustee estimates that its identification and
assessment activities are approximately 80% complete and that its remediation
and testing efforts are approximately 80% complete.  It expects that all of its
Year 2000 efforts related to the Trust's internal systems will be completed by
the end of the first quarter of 1999.  However, there can be no guarantee that
the Trustee will be able to identify all potential Year 2000 problems or to
fully remediate all Year 2000 problems identified on a timely basis.  There
also can be no assurance that the systems of third party vendors on which the
Trust relies will be timely remediated.  The failure by the Trustee or any such
third party to fully remediate its Year 2000 problems on a timely basis could
have a material adverse affect on the Trustee's ability to account for and make
timely distribution of the Trust's distributable income.

Forward-Looking Statements

         This report on Form 10-Q includes "forward-looking statements" within
the meaning of Section 27A of the Securities Act of 1933, as amended, and
Section 21E of the Securities Exchange Act of 1934, as amended.  All statements
other than statements of historical fact included in this Form 10-Q, including,
without limitation, statements contained in this "Trustee's Discussion and
Analysis of Financial Condition and Results of Operations" regarding the
Trust's financial position and industry conditions, are forward-looking
statements.  Although the Trustee believes that the expectations reflected in
such forward-looking statements are reasonable, it can give no assurance that
such expectations will prove to have been correct.

                          PART II - OTHER INFORMATION

Item 3.     Quantitative and Qualitative Disclosures About Market Risk

            Not applicable.





                                       19
<PAGE>   20
Item 6.  Exhibits and Reports on Form 8-K.

         (a)     Exhibit No.             Description

                    27              Financial Data Schedule

         (b)     No reports on Form 8-K were filed during the quarter for which
                 this report is filed.





                                       20
<PAGE>   21
                                   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.

                                    WILLIAMS COAL SEAM GAS ROYALTY TRUST

                                    By:   NATIONSBANK, N.A., Trustee



                                          By:  /s/ Ron Hooper                  
                                               --------------------------------
                                               Ron Hooper
                                               Vice President and Administrator


              (The Trust has no directors or executive officers.)


Date:  November 13, 1998





                                       21
<PAGE>   22
                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT
NUMBER                            DESCRIPTION
-------                           -----------
 <S>                      <C>
  27                       Financial Data Schedule
</TABLE>