<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 June 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 August 1, 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 thereto incorporated by reference 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 June 30, 1998, the distributable income for the
three-month and six-month periods ended June 30, 1998 and 1997, and the changes
in trust corpus for the six-month periods ended June 30, 1998 and 1997, have
been included.  The distributable income for such interim periods is not
necessarily indicative of the distributable income for the full year.

       The financial statements as of June 30, 1998 and for the three-month
and six-month periods ended June 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 of Texas, N.A.
  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 June 30,
1998, and the related condensed statements of distributable income for the
three-month and six-month periods ended June 30, 1998 and 1997, and the
statements of changes in trust corpus for the six-month period ended June 30,
1998 and 1997.  These financial statements are the responsibility of the
Trustee.

We conducted our reviews in accordance with standards established by the
American Institute of Certified Public Accountants.  A review of interim
financial information consists principally of applying analytical procedures to
financial data, and making inquiries of persons responsible for financial and
accounting matters.  It is substantially less in scope than an audit conducted
in accordance with generally accepted auditing standards, 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
August 11, 1998





                                       3
<PAGE>   4
WILLIAMS COAL SEAM GAS ROYALTY TRUST

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

<TABLE>
<CAPTION>
                                                     June 30,        December 31,
ASSETS                                                 1998             1997 
                                                    -----------      -----------
<S>                                                 <C>              <C>        
Current Assets -
       cash and cash equivalents                    $     1,227      $    30,636
Royalty interests in oil
       and gas properties
       (less accumulated
       amortization of
       $83,071,073 at
       June 30, 1998
       and $77,150,886 at
       December 31, 1997)                            55,495,591       61,415,777
                                                    -----------      -----------

TOTAL ASSETS                                        $55,496,818      $61,446,413
                                                    ===========      ===========

LIABILITIES AND TRUST CORPUS

Current Liabilities -
       trust expenses payable                       $   155,139      $   174,713

Trust corpus -
       9,700,000 units of
       beneficial interest
       authorized and
       outstanding                                   55,341,679       61,271,700
                                                    -----------      -----------

TOTAL LIABILITIES
       AND TRUST CORPUS                             $55,496,818      $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
                                              June 30, 1998        June 30, 1997  
                                              -------------        -------------
<S>                                            <C>                  <C>        
Royalty income                                 $ 5,411,826          $ 6,075,355
Interest income                                     20,235               23,698
                                               -----------          -----------
                                                 5,432,061            6,099,053

General and administrative
       expenses                                   (265,891)            (231,077)
                                               -----------          -----------
Distributable income $                           5,166,170          $ 5,867,976
                                               -----------          -----------

Distributable income
       per unit
       (9,700,000 units)                       $       .53          $       .60
                                               -----------          -----------
</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>
                                             SIX MONTHS             SIX MONTHS
                                                ENDED                 ENDED
                                            June 30, 1998         June 30, 1997  
                                            -------------         -------------
<S>                                          <C>                   <C>         
Royalty income                               $  8,460,122          $ 10,179,169
Interest income                                    29,801                35,884
                                             ------------          ------------
                                                8,489,923            10,215,053

General and administrative
       expenses                                  (389,835)             (418,211)
                                             ------------          ------------
Distributable income $                          8,100,088          $  9,796,842
                                             ============          ============

Distributable income
       per unit
       (9,700,000 units)                     $        .83          $       1.01
                                             ============          ============
</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>
                                              SIX MONTHS           SIX MONTHS
                                                 ENDED                ENDED
                                             June 30, 1998        June 30, 1997 
                                             --------------      --------------
<S>                                          <C>                 <C>           
Trust corpus,                                $   61,271,700      $   70,021,573
       beginning of period
Amortization of royalty
       interests                                 (5,920,186)         (4,023,493)
Distributable income                              8,100,088           9,796,842
Distributions to Unitholders                     (8,109,923)         (9,955,053)
                                             --------------      --------------


Trust corpus, end
       of period                             $   55,341,679      $   65,839,869
                                             ==============      ==============

Distributions per unit
       (9,700,000 units)                     $          .84      $         1.03
                                             ==============      ==============
</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 NationsBank, 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") formerly
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 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").





                                       8
<PAGE>   9
       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 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





                                       9
<PAGE>   10
(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 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





                                       10
<PAGE>   11
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.

       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





                                       11
<PAGE>   12
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.

5.     SUBSEQUENT EVENTS

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

<TABLE>
<CAPTION>
        Quarterly
         Record        Payment     Distribution
          Date          Date         per Unit  
       ----------    ----------    ------------
       <S>           <C>           <C>
       August 14     August 28     $.473926
</TABLE>

       The distribution per unit decreased from $.533202 in the second quarter
of 1998 to $.473926 in the third quarter of 1998.  The decrease in
distributions was mainly due to adjustments for federal unit acreage expansion
during prior periods.  The distributions were also impacted by a decrease in 
gross proceeds due to lower volumes offset by a decrease in capital
expenditures. 

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 second quarter of 1998, the applicable index price was above
the Minimum Purchase Price resulting in recoupments against the price credit
account established pursuant to the terms of the Gas Purchase Contract.  WPC
estimates that, as of June 30, 1998, WFS Gas Resources had aggregate price
credits in the price credit account of approximately $11.4 million





                                       12
<PAGE>   13
of which the Trust's 81 percent interest was approximately $9.2 million.  The
applicable index price was above the Minimum Purchase Price in July 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.

       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 of which these Notes to Financial Statements are a part
(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 158.3 Bcf. Based upon
projections of reserves by Miller and Lents, Ltd., the Trust's independent
petroleum engineers, WPC does not currently expects the internal rate of return
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 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.





                                       13
<PAGE>   14
       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 WPC and not the Trust.

       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.





                                       14
<PAGE>   15
Three Months and Six Months Ended June 30, 1998 Compared to Three Months and
Six Months Ended June 30, 1997

       For the quarter ended June 30, 1998, royalty income received by the
Trust amounted to $5,411,826 as compared to $6,075,355 received for the same
quarter in 1997. The decrease in royalty income is due to lower proceeds from
the Farmout Properties due to higher prices and higher production volumes in
1997. This decrease was offset by adjustments resulting from expansion of 
federal units within the Underlying Properties during prior periods.
Additionally, royalty income was impacted by a net increase in net revenue
deductions due to a decrease in price compared to 1997, partially offset by
increased capital expenditure deductions in 1998. Royalty income for the six
months ended June 30, 1998 was $8,460,122 as compared to $10,179,169 for the
same period in 1997.  Adjustments in the federal units and overall production
decline resulted in lower royalty income for the six months ended June 30, 1998.
Interest income for the quarter ended June 30, 1998 was $20,235 compared to
$23,698 for the same quarter in 1997.  Interest income for the six months ended
June 30, 1998 was $29,801 as compared to $35,884 for the same period in 1997.
General and administrative expenses during the second quarter of 1998 amounted
to $265,891 compared to $231,077 for the same quarter in 1997. General and
administrative expenses for the six months ended June 30, 1998 were $389,835 as
compared to $418,211 for the same period in 1997.

Distributable income for the quarter ended June 30, 1998 was $5,166,170
or $.53 per Unit compared to $5,867,976 or $.60 per Unit for the second quarter
of 1997.  This decrease was the result of adjustments resulting from expansion
of federal units within the Underlying Properties.  A distribution of $.533202
per Unit was made on May 29, 1998 to Unitholders of record on May 15, 1998.
Distributable income for the six months ended June 30, 1998 was $8,100,088 as
compared to $9,796,842 for the same period in 1997. This decrease was the
result of the aforementioned reasons as stated above.

       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, 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,





                                       15
<PAGE>   16
in the month immediately following such calendar quarter.  Accordingly, the
royalty income included in distributable income for the quarter ended June 30,
1998 was based on production volumes and natural gas prices for the period
January 1998 through March 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 second quarter of 1998 reflects estimated
production volumes from the Farmout Properties for the months of December 1997
through February 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
                                           March 31, 1998       March 31, 1997
                                           --------------       --------------
<S>                                        <C>                  <C>          
Production (MMBtu)(1)
     WI Properties                             5,994,326(2)         2,961,685(4)
     Farmout Properties                        1,287,499(3)         1,770,506(5)


Blanco Hub Spot Price
     ($/MMBtu)(6)                          $        1.94        $        2.47
Net Wellhead Price
     WI Properties ($/MMBtu)(6)            $        1.01        $        1.09
</TABLE>

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

(1)    Million British Thermal Units.

(2)    Includes prior period adjustments of 2,792,966 MMBtu increase.

(3)    Reflects estimated volumes for December 1997 through February 1998.

(4)    Includes prior period adjustments of 1,194,525 MMBtu increase.

(5)    Reflects actual volumes for December 1996 through February 1997.

(6)    Simple average of 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 ("WFS Gas
Resources") (as successor in interest to Williams Gas Marketing Company) (as
amended, the "Gas Purchase Contract").  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





                                       16
<PAGE>   17
"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 Primary Term will therefore remain in place
through at least December 31, 1998.

       The Blanco Hub Spot Price was above $1.75 per MMBtu during January,
February and March 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 recouped price credits for each MMBtu of natural gas so
purchased 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 March 31, 1998,
WFS Gas Resources had aggregate price credits of approximately $11.9 million of
which the Trust's 81 percent interest was approximately $9.6 million.  The
Blanco Hub Spot Price was above $1.75 per MMBtu in July  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.

       The Blanco Hub Spot Price was above 1.75 per MMBtu during April, May and
June, 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 recouped price credits for each MMBtu of natural gas so
purchased 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 June 30, 1998,
WFS Gas Resources had aggregate price credits of approximately $11.4 million of
which the Trust's 81 percent interest was approximately $9.2 million.  The
Blanco Hub Spot Price was above $1.75 per MMBtu in July 1998.

       The entitlement of WFS Gas Resources o 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.





                                       17
<PAGE>   18
       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.

       Year 2000 Issue

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

       The Trust is reliant on the performance of Williams and third party
vendors for the receipt of royalty income, payment of expenses and disbursement
of distributable income.  The Trustee can provide no assurance as to whether
Williams and third party vendors will successfully address the Year 2000 issue.
Failing to successfully address the Year 2000 issue by Williams and third party
vendors could have a material adverse impact on the Trust and its Unitholders.

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.

Item 3.       Quantitative and Qualitative Disclosures About Market Risk.

       Not applicable.





                                       18
<PAGE>   19
                          PART II - OTHER INFORMATION

Item 1.       Legal Proceedings

              The following discussion concerns a material development in a
              legal matter which may effect the Trust and which occurred
              subsequent to June 30, 1998.

       Southern Ute Litigation.  As previously reported in the Public Offering
Prospectus, each of the Trust's prior Annual Reports on Form 10-K as filed with
the SEC, and most recently in the Trust's 1997 Annual Report on Form 10-K (the
"1997 Annual Report") under "Item 2--The Royalty Interest--Title to Properties-
-Southern Ute Litigation," WPC has been named as a defendant in a lawsuit
brought by the Southern Ute Indian Tribe (the "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
following information is included herein for the purpose of updating the
disclosure provided in the 1997 Annual Report as a result of the ruling issued
July 20, 1998, with respect to the March 17, 1998 rehearing en banc of the
United States Court of Appeals for the Tenth Circuit (the "Court of Appeals")
and should be read in conjunction with the discussion of the litigation
provided in the 1997 Annual Report.  Capitalized terms used and not otherwise
defined in the following discussion are used with the meanings given to such
terms in the 1997 Annual Report.

       On December 31, 1991, the Tribe initiated the Southern Ute Litigation in
the United States District Court for the District of Colorado (the "District
Court") against WPC, Amoco Production Company ("Amoco") and other major gas
producers and affected parties in the San Juan Basin area (collectively, the
"Defendant Class"), alleging that certain coal strata and constituents within
that strata (including coal seam gas) were reserved by the United States, then
granted to the Tribe for the Tribe's perpetual benefit and ownership.  The
Tribe alleges that coal seam gas from the coal strata is being and has been
wrongfully extracted by the Defendant Class.  The Tribe is seeking a
declaration that it owns a beneficial interest in the coal seam gas and that
the extraction of such gas without Tribal consent is an unlawful trespass.  In
addition to a declaration of ownership of the gas, the Tribe is seeking
compensation for the value of coal seam gas heretofore extracted and certain
other remedies.

       The Southern Ute Litigation involves approximately 1,745 gross acres
comprising a portion of the Farmout Properties. Two Tribe leases covering
approximately 3,600 gross acres included in the Farmout Properties are not
covered by the pending litigation, but could be the subject of future
litigation.

       Amoco, on behalf of itself, WPC and the other members of the Defendant
Class, is vigorously defending the lawsuit.  On September 13, 1994, the
District Court issued a memorandum opinion and order in the litigation granting
the motion for summary judgment filed by the Defendant Class on the question of
ownership of the coal seam gas.  The District Court ruled that the U.S.
Congress did not reserve the coal seam gas in the Coal Lands Acts of 1909 and





                                       19
<PAGE>   20
1910, and denied the Tribe's claims of equitable ownership of the coal seam
gas.  The Tribe appealed the order to the United States Court of Appeals for
the Tenth Circuit (the "Court of Appeals"), which issued an opinion dated July
16, 1997 reversing the District Court and holding that coal seam gas was "an
integral component of coal" and had therefore been vested in the Tribe as
owners of the coal resource.  The Court of Appeals remanded the matter to the
District Court for further proceedings consistent with its decision.  Amoco, as
class representative of the Defendant Class, subsequently sought and obtained a
rehearing en banc from the Court of Appeals on the ownership issue.  The en
banc hearing was held on March 17, 1998, and on July 20, 1998, a decision on
the hearing was issued upholding the original opinion of the Court of Appeals
finding ownership in the Tribe.  Amoco has indicated its intent to seek
additional review of the Court for Appeals' decision.  If any such further
review is sought and denied, District Court proceedings would then be conducted
to adjudicate the respective affirmative defenses of the members of the
Defendant Class to the Tribe's claims.

       Unitholders should consult the 1997 Annual Report for additional
information concerning the Southern Ute Litigation and its possible
consequences to the Trust and its Unitholders.  The Trustee makes no prediction
as to ultimate resolution of this litigation or as to the likely effect, if
any, that such resolution may have upon the Trust or its Unitholders.

Item 5.  Other Information.

       Effective May 6, 1998, NationsBank of Texas, N.A., of Dallas, Texas,
merged with NationsBank, N.A., of Charlotte, North Carolina.  NationsBank,
N.A., as survivor of the merger, has assumed by operation of law all rights,
properties and interests of NationsBank of Texas, N.A., including all rights
and interests as trustee, executor or administrator or in other fiduciary
capacities, in the same manner and to the same extent as such rights,
properties and interests were held by NationsBank of Texas, N.A. at the time of
the merger.  In accordance with applicable law and the provisions of the Trust
Agreement, NationsBank, N.A., as successor to NationsBank of Texas, N.A., now
serves as Trustee of the Trust.  NationsBank, N.A. is performing such functions
through its Dallas, Texas, branch office, which is the former principal office
of NationsBank of Texas, N.A.

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:  August 13, 1998





                                       21

<PAGE>   22
                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
              Exhibit No.                         Description
              -----------                         -----------
                   <S>                            <C>
                   27                             Financial Data Schedule
</TABLE>


                                       22