<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 March 31, 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: 001-11335

                     DOMINION RESOURCES BLACK WARRIOR TRUST
             (Exact name of registrant as specified in its charter)


          Delaware                                          75-6461716
(State or other jurisdiction                              (I.R.S. Employer
    or incorporation or                                  Identification No.)
       organization)



                           NationsBank of Texas, N.A.
                                 901 Main Street
                                   17th Floor
                               Dallas, Texas 75202
                    (Address of principal executive offices)
                                   (Zip code)

                                 (214) 508-2400
              (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 May 1, 1998:
7,850,000

<PAGE>   2

                         PART I - FINANCIAL INFORMATION


Item 1.  Financial Statements.

         The condensed financial statements included herein have been prepared
by NationsBank of Texas, N.A., as Trustee (the "Trustee") of Dominion Resources
Black Warrior 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. The
condensed financial statements of the Trust presented herein are unaudited
except for the balances as of December 31, 1997, and, therefore, are subject to
year-end adjustments. It is suggested that these condensed financial statements
be read in conjunction with the financial statements and notes thereto in the
Trust's 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 as of that
date. In the opinion of the Trustee, all adjustments consisting of normal
recurring adjustments necessary to present fairly the assets, liabilities and
trust corpus of the Trust as of March 31, 1998, the distributable income for the
three-month periods ended March 31, 1998 and 1997 and the changes in trust
corpus for the three-month periods ended March 31, 1998 and 1997, have been
included. The distributable income for such interim periods are not necessarily
indicative of the distributable income for the full year.

         The condensed financial statements as of March 31, 1998 and for the
three-month periods ended March 31, 1998 and 1997 included herein have been
reviewed by Deloitte & Touche LLP, independent certified public accountants, as
stated in their report appearing herein.



                                       -2-

<PAGE>   3

                         INDEPENDENT ACCOUNTANTS' REPORT

NationsBank of Texas, N.A.,
  as Trustee of Dominion Resources
  Black Warrior Trust

We have reviewed the accompanying condensed statement of assets, liabilities and
trust corpus of Dominion Resources Black Warrior Trust as of March 31, 1998, and
the related condensed statements of distributable income and changes in trust
corpus for the three-month periods ended March 31, 1998 and 1997. These
financial statements are the responsibility of the Trustee.

We conducted our review 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 of making inquiries of persons responsible for financial and accounting
matters. It is substantially less in scope than an audit conducted in accordance
with generally accepted auditing standards, the objective of which is the
expression of an opinion regarding the financial statements taken as a whole.
Accordingly, we do not express such an opinion.

As described in Note 2 to the condensed financial statements, these condensed
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 review, we are not aware of any material modifications that should
be made to such condensed financial statements for them to be in conformity with
the basis of accounting described in Note 2.

We have previously audited, in accordance with generally accepted auditing
standards, the statement of assets, liabilities and trust corpus of Dominion
Resources Black Warrior 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 4, 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.

/s/ Deloitte & Touche LLP

Dallas, Texas
May 11, 1998



                                       -3-

<PAGE>   4

DOMINION RESOURCES BLACK WARRIOR TRUST

CONDENSED STATEMENTS OF ASSETS,
LIABILITIES AND TRUST CORPUS

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

<TABLE>
<CAPTION>
                                            March 31, 1998   December 31, 1997
                                            --------------   -----------------
                                             (unaudited)
<S>                                         <C>               <C>
ASSETS

Cash and cash equivalents                   $    51,150       $    54,431
Royalty interests in
  gas properties (less accumulated
  amortization of $60,957,841
  at March 31, 1998 and $58,097,578
  at December 31, 1997)                      94,859,659        97,719,922
                                            -----------       -----------

TOTAL ASSETS                                $94,910,809       $97,774,353
                                            ===========       ===========


LIABILITIES AND TRUST CORPUS

Trust administration expenses payable       $   218,873       $   103,652

Trust corpus -
         7,850,000 units of
         beneficial interest
         authorized, issued and
         outstanding                         94,691,936        97,670,701
                                            -----------       -----------

TOTAL LIABILITIES
         AND TRUST CORPUS                   $94,910,809       $97,774,353
                                            ===========       ===========
</TABLE>

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



                                       -4-

<PAGE>   5

DOMINION RESOURCES BLACK WARRIOR TRUST

CONDENSED STATEMENTS OF DISTRIBUTABLE INCOME (UNAUDITED)

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

<TABLE>
<CAPTION>
                                             For                For
                                          the Three          the Three
                                         Months Ended       Months Ended
                                        March 31, 1998    March 31, 1997
                                        --------------    --------------
<S>                                      <C>                <C>        
Royalty income                           $ 6,917,233        $ 6,796,794
Interest income                               24,710             17,302
                                         -----------        -----------
                                           6,941,943          6,814,096

General and administrative
        expenses                            (193,101)          (198,056)
                                         -----------        -----------
Distributable income                     $ 6,748,842        $ 6,616,040
                                         ===========        ===========

Distributable income
        per unit (7,850,000 units)       $       .86        $       .84
                                         ===========        ===========
</TABLE>



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



                                       -5-
<PAGE>   6



DOMINION RESOURCES BLACK WARRIOR TRUST

CONDENSED STATEMENTS OF CHANGES IN TRUST CORPUS (UNAUDITED)

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

<TABLE>
<CAPTION>
                                                    For                   For
                                                 the Three             the Three
                                                Months Ended         Months Ended
                                               March 31, 1998       March 31, 1997
                                               --------------       --------------
<S>                                            <C>                  <C>          
Trust corpus, beginning of period              $  97,670,701        $ 109,562,077
Amortization of royalty interests                 (2,860,263)          (3,962,004)
Distributable income                               6,748,842            6,616,040
Distributions to unitholders                      (6,867,344)          (6,626,775)
                                               -------------        -------------
Trust corpus, end of period                    $  94,691,936        $ 105,589,338
                                               =============        =============


Distributions per unit (7,850,000 units)       $         .87        $         .84
                                               =============        =============
</TABLE>

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



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



                                       -6-
<PAGE>   7



DOMINION RESOURCES BLACK WARRIOR TRUST

NOTES TO CONDENSED FINANCIAL STATEMENTS (UNAUDITED)

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

1.      TRUST ORGANIZATION AND PROVISIONS

        Dominion Resources Black Warrior Trust (the "Trust") was formed as a
Delaware business trust pursuant to the terms of the Trust Agreement of Dominion
Resources Black Warrior Trust (as amended, the "Trust Agreement") entered into
effective as of May 31, 1994, by and among Dominion Black Warrior Basin, Inc.,
an Alabama corporation (the "Company"), as trustor, Dominion Resources, Inc., a
Virginia corporation ("Dominion Resources"), and NationsBank of Texas, N.A., a
national banking association (the "Trustee"), and Mellon Bank (DE) National
Association, a national banking association (the "Delaware Trustee"), as
trustees. The trustees are independent financial institutions.

        The Trust is a grantor trust formed to acquire and hold certain
overriding royalty interests (the "Royalty Interests") burdening proved natural
gas properties located in the Pottsville coal formation of the Black Warrior
Basin, Tuscaloosa County, Alabama (the "Underlying Properties") owned by the
Company. The Trust was initially created by the filing of its Certificate of
Trust with the Delaware Secretary of State on May 31, 1994. In accordance with
the Trust Agreement, the Company contributed $1,000 as the initial corpus of the
Trust. On June 28, 1994, the Royalty Interests were conveyed to the Trust by the
Company pursuant to the Overriding Royalty Conveyance (the "Conveyance") dated
effective as of June 1, 1994, from the Company to the Trust, in consideration
for all the 7,850,000 authorized units of beneficial interest ("Units") in the
Trust. The Company transferred its Units to its parent, Dominion Energy, Inc., a
Virginia corporation, which in turn transferred such Units to its parent,
Dominion Resources, which sold 6,850,000 of such Units to the public through
various underwriters (the "Underwriters") in June 1994 and an additional 54,000
Units through the Underwriters in August 1994 (collectively, the "Public
Offering"). The remaining 946,000 Units held by Dominion Resources were sold to
the public through certain of the Underwriters in June 1995 pursuant to
Post-Effective Amendment No. 1 to the Form S-3 Registration Statement relating
to the Units (the "Post-Effective Amendment"). All of the production
attributable to the Underlying Properties is from the Pottsville coal formation
and currently constitutes coal seam gas that entitles the owners of such
production, provided certain requirements are met, to tax credits pursuant to
Section 29 of the Internal Revenue Code of 1986, as amended, upon the production
and sale of such gas.

        Royalty income to the Trust is attributable to the sale of depleting
assets. All of the Underlying Properties consist of producing properties.
Accordingly, the proved reserves attributable to 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.



                                       -7-

<PAGE>   8



        The Trustee has all powers to collect and distribute 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 or are required by law
and is not empowered to otherwise manage or take part in the management 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 or the Company's interest therein.

        The Trust is subject to termination under certain circumstances
described in the Trust Agreement. Upon the termination of the Trust, all Trust
assets will be sold and the net proceeds therefrom distributed to Unitholders.

        The only assets of the Trust, other than cash and temporary investments
being held for the payment of expenses and liabilities and for distribution to
Unitholders, are the Royalty Interests. The Royalty Interests consist of
overriding royalty interests burdening the Company's interest in the Underlying
Properties. The Royalty Interests generally entitle the Trust to receive 65
percent of the Company's Gross Proceeds (as defined below). The Royalty
Interests are non-operating interests and bear only expenses related to
property, production and related taxes (including severance taxes). "Gross
Proceeds" consist generally of the aggregate amounts received by the Company
attributable to the interests of the Company in the Underlying Properties from
the sale of coal seam gas at the central delivery points in the gathering system
for the Underlying Properties. The definitions, formulas and accounting
procedures and other terms governing the computation of the Royalty Interests
are set forth in the Conveyance.

        Because of the passive nature of the Trust and the restrictions and
limitations on the powers and activities of the Trustee contained in the Trust
Agreement, the Trustee does not consider any of the officers and employees of
the Trustee to be "officers" or "executive officers" of the Trust as such terms
are defined under applicable rules and regulations adopted under the Securities
Exchange Act of 1934.

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:

-       Royalty income and interest income are recorded in the period in which
        amounts are received by the Trust rather than in the period of
        production and accrual, respectively.

-       General and administrative expenses recorded are based on liabilities
        paid and cash reserves established out of cash received.

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



                                       -8-

<PAGE>   9



-       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, general and administrative expenses recorded are based on
liabilities paid and cash reserves established rather than on an accrual basis,
and amortization of the Royalty Interests is not charged against operating
results.

        The net amount of royalty interests in gas properties is limited to the
sum of the future net cash flows attributable to the Trust's gas reserves using
current unescalated product prices plus the estimated future Section 29 credits
for federal income tax purposes. If the net cost of royalty interests in gas
properties exceeds this amount, an impairment provision will be recorded and
charged to the trust corpus.

3.      FEDERAL INCOME TAXES

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

        Because the Trust is treated as a grantor trust, and because a
Unitholder is treated as directly owning an interest in the Royalty Interests,
each Unitholder will be taxed directly on his per Unit 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 a 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 calendar 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 attributable to production from the Royalty Interests
during such quarter, provided that such cash is received by the Trust on or
before the last business day prior to the 45th day following the end of such
calendar quarter, plus the amount of interest expected by the Trustee to be
earned on such cash proceeds during the period between the date of receipt by
the Trust of such cash proceeds and the date of payment to



                                       -9-

<PAGE>   10



the Unitholders of such Quarterly Distribution Amount, plus all other cash
receipts of the Trust during such quarter (to the extent not distributed or held
for future distribution as a Special Distribution Amount (as defined below) or
included in the previous Quarterly Distribution Amount) (which might include
sales proceeds not sufficient in amount to qualify for a special distribution as
described in the next paragraph and interest), over the liabilities of the Trust
paid during such quarter and not taken into account in determining a prior
Quarterly Distribution Amount, 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. An amount which is not included
in the Quarterly Distribution Amount for a calendar quarter because such amount
is received by the Trust after the last business day prior to the 45th day
following the end of such calendar quarter will be included in the Quarterly
Distribution Amount for the next calendar quarter. The Quarterly Distribution
Amount for each quarter will be payable to Unitholders of record on the 60th 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
will distribute the Quarterly Distribution Amount for each calendar quarter on
or prior to 70 days after the end of such calendar quarter to each person who
was a Unitholder of record on the record date for such calendar quarter.

        The Royalty Interests may be sold under certain circumstances and will
be sold following termination of the Trust. A special distribution will be made
of undistributed net sales proceeds and other amounts received by the Trust
aggregating in excess of $10 million (a "Special Distribution Amount"). The
record date for a Special Distribution Amount will be the 15th day following the
receipt by the Trust of amounts aggregating a Special Distribution Amount
(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 or less
prior to the record date for a Quarterly Distribution Amount, in which case the
record date will be the date that 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.

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

        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 certain
overriding royalty interests (the "Royalty Interests") burdening certain proved
natural gas properties located in the Pottsville coal formation of the Black
Warrior Basin, Tuscaloosa County, Alabama (the "Underlying Properties"). The
Royalty Interests owned by the Trust burden the interest in the Underlying
Properties that is owned by Dominion Black Warrior Basin, Inc. (the "Company"),
an indirect wholly owned subsidiary of Dominion Resources, Inc.
("Dominion Resources").

        Distributable income of the Trust consists of the excess of royalty
income plus interest income over the organizational and administrative expenses
of the Trust. Upon receipt by the Trust, royalty income is invested in
short-term investments in accordance with the Trust



                                      -10-

<PAGE>   11

Agreement of Dominion Resources Black Warrior Trust (as amended, the "Trust
Agreement") 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 they are paid or reserves are established for them.
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 paid by the Trust during such quarter. The amount of cash available for
distribution to Unitholders is determined as adjusted for changes in reserves
for unpaid liabilities in accordance with the provisions of the Trust Agreement.
(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 Month Period Ended March 31, 1998 Compared to Three Months Ended March 31,
1997

        The Trust's Royalty Interests consist of overriding royalty interests
burdening the Company's interest in the Underlying Properties. The Royalty
Interests generally entitle the Trust to receive 65 percent of the Company's
Gross Proceeds (as defined below) during the preceding calendar quarter. The
Royalty Interests are non-operating interests and bear only expenses related to
property, production and related taxes (including severance taxes). "Gross
Proceeds" consist generally of the aggregate amounts received by the Company
attributable to the interests of the Company in the Underlying Properties from
the sale of coal seam gas at the central delivery points in the gathering system
for the Underlying Properties. The definitions, formulas and accounting
procedures and other terms governing the computation of the Royalty Interests
are set forth in the Overriding Royalty Conveyance from the Company to the
Trust.

        The Trust received royalty income amounting to $6,917,233 during the
first quarter of 1998 compared to $6,796,794 during the first quarter of 1997.
This revenue was derived from the receipt of cash on production of 2,765 Mmcf at
an average price received of $2.65 per mcf after deducting production taxes of
$419,670 compared to 2,978 Mmcf with an average price of $2.41 per mcf after
deducting production taxes of $392,850 in the first quarter of 1997. For the
three-month period ended March 31,1998, the Trust was positively impacted by the
increase in natural gas prices offsetting the decline in production between
these two periods. These prices are influenced by many factors such as seasonal
temperatures, domestic demand and other factors that are beyond the control of
the Trustee. The decrease in production is attributed to normal depletion of
existing available reserves. Production taxes are based on revenues rather than
production volumes. Accordingly, production taxes did not fluctuate
proportionately to the decrease in volumes.

        Administrative expenses during the first quarter of 1998 amounted to
$193,101 compared to $198,056 in the comparable period in 1997. This decrease in
administrative expenses was



                                      -11-

<PAGE>   12

caused by the timing of payment of certain professional expenses. For this
period, these expenses were primarily related to administrative services
provided by Dominion Resources and the Trustee and Mellon Bank (DE) National
Association, a national banking association, and the preparation of year-end
reports for submission to the Securities and Exchange Commission and to
Unitholders during the period.

        Distributable income for the first quarter of 1998 was $6,748,842 or
$.86 per Unit compared to distributable income for the first quarter of 1997 of
$6,616,040 or $.84 per Unit. The Trust made a distribution on March 11, 1998 of
$.874820 per Unit compared to a distribution of $.844175 per Unit made during
the first quarter of 1997.

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 Dominion Resources 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 Dominion Resources and third party vendors will successfully address the
Year 2000 issue. Failing to successfully address the year 2000 issue by Dominion
Resources and third party vendors could have a material adverse impact on the
Trust and its Unitholders. The Trust is making every effort that the systems
under its direct control are being addressed and will be ready for year 2000.

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.

        Inapplicable.



                                      -12-

<PAGE>   13



                           PART II - OTHER INFORMATION


Item 5.  Other Information.

        The following is a description of an action taken by the Company
subsequent to March 31, 1998, regarding marketing arrangements for the gas
produced from the Underlying Properties for calendar year 1999.  Capitalized
terms used below and not otherwise defined herein are used with the meanings
given them in the Trust's Annual Report on Form 10-K for the year ended December
31, 1997 (the "1997 Form 10-K").

        By letter dated April 21, 1998, Dominion Energy, Inc. ("Dominion
Energy"), the indirect parent of the Company, notified the Trustee that the
Company has entered into an arrangement with Sonat Marketing regarding the sale
by the Company of Subject Gas for calendar year 1999. Under this arrangement,
during calendar year 1999, Sonat Marketing's gas purchases from the Company for
volumes up to the amount of certain Monthly Fixed Price Quantities (equal to
1,300,000 MMBtu for January through May and 1,200,000 MMBtu for June through
December) will be paid at the Index Price, subject to a minimum Index Price of
$2.10 and a maximum Index Price of $3.00 per MMBtu, plus the applicable Premium
established by the terms of the current Gas Purchase Agreement. For purchases of
gas in excess of the applicable Monthly Fixed Price Quantity, Sonat Marketing
will purchase such additional monthly volumes at a price equal to the Index
Price (without any minimum or maximum) plus a $.02 per MMBtu premium.  While the
establishment of a minimum Index Price for 1999 assures the Unitholder a minimum
price at which the Monthly Fixed Price Quantity will be paid, until January 1,
2000, Unitholders will benefit from natural gas prices in excess of $3.00 per
MMBtu only to the extent of sales in excess of such monthly quantities. The
Trust has been advised that the Company and Sonat Marketing are in the process
of finalizing an amendment to the Gas Purchase Agreement regarding the calendar
year 1999 pricing arrangement described above. Sonat Marketing has notified the
Company that it has entered into put and call arrangements to minimize its
potential losses as a result of these minimum price provisions.

        The Gas Purchase Agreement is described in more detail in the 1997 Form
10-K and is filed as an exhibit thereto.  It is recommended that Unitholders
consider the foregoing summary in the context of the relevant disclosure set
forth in the 1997 Form 10-K, particularly "Item 2--The Royalty Interests--Gas
Purchase Agreement".

Item 6.  Exhibits and Reports on Form 8-K.

        (a) Exhibits

               27            Financial Data Schedule

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



                                      -13-

<PAGE>   14


                                   SIGNATURES

        Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                             DOMINION RESOURCES BLACK
                                             WARRIOR TRUST

                                             By:  NATIONSBANK OF TEXAS, N.A.,
                                                  Trustee



                                             By:  /s/ Ron E. Hooper
                                                  ------------------------------
                                                  Ron E. Hooper
                                                  Vice President


Date: May 13, 1998

              (The Trust has no directors or executive officers.)



                                      -14-

<PAGE>   15

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit
Number                        Description
-------                       -----------
<S>                     <C>
  27                    Financial Data Schedule
</TABLE>