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

                                    FORM 10-Q

[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE 
ACT OF 1934

     For the quarterly period ended September 30, 1998

                                       or

[ ] TRANSITION REPORT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT 
OF 1934

     For the transition period from               to
                                   ---------------   ---------------

                          COMMISSION FILE NO. 333-46843

                      MEWBOURNE ENERGY PARTNERS 98-A, L.P.


         Delaware                                              75-2743955
-----------------------------                             ----------------------
 (State or jurisdiction of                                   (I.R.S. Employer
incorporation or organization)                            Identification Number)


3901 South Broadway, Tyler, Texas                                 75701
--------------------------------------------------------------------------------
(Address of principal executive offices)                        (Zip Code)


Registrant's Telephone Number, including area code:(903) 561-2900

                                 Not Applicable
                                 --------------
             (Former name, former address and former fiscal year, if
                           changed since last report)

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. [X] Yes [ ] No



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                      MEWBOURNE ENERGY PARTNERS 98-A, L. P.

                         Part I - Financial Information


ITEM 1.  FINANCIAL STATEMENTS



                                  BALANCE SHEET
                               September 30, 1998
                                   (Unaudited)


<TABLE>
<CAPTION>



ASSETS
<S>                                                              <C>
Cash                                                              $   100
                                                                  -------

Total assets                                                      $   100
                                                                  =======



PARTNERS' CAPITAL


Partners' capital                                                 $   100
                                                                  -------

Total Partners' capital                                           $   100
                                                                  =======
</TABLE>





                     The accompanying notes are an integral
                       part of the financial statements.




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                      MEWBOURNE ENERGY PARTNERS 98-A, L. P.



                         STATEMENT OF PARTNERS' CAPITAL
               for the period January 27, 1998 (date of inception)
                           through September 30, 1998
                                   (Unaudited)

<TABLE>
<CAPTION>


                                                Limited &  Managing
                                                General    General
                                                Partners   Partner     Total
                                                ---------  --------   --------

<S>                                             <C>        <C>        <C>     
Partners' capital at January 27,
1998 (date of Inception)                        $     --   $     --   $     --

Contributions                                   $    100   $     --   $    100
                                                --------   --------   --------

Partners' capital at
  September 30, 1998                            $    100   $     --   $    100
                                                ========   ========   ========
</TABLE>





                     The accompanying notes are an integral
                       part of the financial statements.




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<PAGE>   4





                      MEWBOURNE ENERGY PARTNERS 98-A, L. P.




                             STATEMENT OF CASH FLOWS
               for the period January 27, 1998 (date of inception)
                           through September 30, 1998
                                   (Unaudited)


<TABLE>


<S>                                                      <C>
Cash flows from financing activities:

  Capital contributions from partners                     $    100
                                                          --------

Cash, end of period                                       $    100
                                                          ========
</TABLE>












                     The accompanying notes are an integral
                       part of the financial statements.

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<PAGE>   5






                      MEWBOURNE ENERGY PARTNERS 98-A, L.P.


                          NOTES TO FINANCIAL STATEMENTS
                                   (Unaudited)


1.       The financial statements reflect all adjustments which are, in the
         opinion of management, necessary for a fair statement of results. All
         adjustments are of a normal recurring nature.

2.       Mewbourne Energy Partners 98-A, L.P. (the "Registrant") was formed
         January 27, 1998. As of September 30, 1998, the only financial activity
         that had occurred was the receipt of the organizational contribution of
         $100. The offering of limited and general partnership interests began
         on May 14, 1998. As of November 4, 1998, interests aggregating
         $1,323,000 had been sold to 59 subscribers of which $1,273,000 were
         sold to 56 subscribers as general partner interests and $50,000 were
         sold to 3 subscribers as limited partner interests.

3.       From the period commencing January 27, 1998 to September 30, 1998, the
         Registrant conducted no business activity. Therefore, there are no 
         items of income or expense for the reporting period and, accordingly a 
         statement of income is not provided.














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<PAGE>   6





ITEM 2.          MANAGEMENTS'S DISCUSSION AND ANALYSIS OF FINANCIAL
                       CONDITION AND RESULTS OF OPERATIONS

Mewbourne Energy Partners 98-A, L.P. was formed January 27, 1998. Mewbourne
Development Corporation is the Managing Partner, and has the power and authority
to manage, control and administer all partnership affairs. As of September 30,
1998, the only financial activity which had occurred was the receipt of the
organizational contribution of $100. The offering of limited and general
partnership interests began on May 14, 1998. As of November 4, 1998, interests
aggregating $1,323,000 had been sold to 59 subscribers of which $1,273,000 were
sold to 56 subscribers as general partner interests and $50,000 were sold to 3
subscribers as limited partner interests.


RESULTS OF OPERATIONS

The Registrant had not commenced operations prior to the period ended September
30, 1998, therefore, no trend analysis based on quarterly changes in results of
operations is available.


LIQUIDITY AND CAPITAL RESOURCES

The Registrant was formed on January 27, 1998, and the organizational
contribution of $100 in cash was contributed to the Registrants's capital.
During the period after formation that ended September 30, 1998, there was no
increase in cash and there were no distributions to partners.





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YEAR 2000 ISSUE

Due to the fact the partnership has no accounting systems of its own, it is not
directly impacted by any potential Year 2000 issues. Substantially all of the
partnership's financial results, however, are derived from the accounting
systems of Mewbourne Oil Company,("MOC"). MOC has made an assessment of the
impact of the Year 2000 on its financial and operational systems and is in the
process of upgrading its systems to those which the corresponding vendors have
certified are Year 2000 compliant. The cost of these upgrades, which are
estimated to be completed by June 1, 1999, are not expected to be materially
different from the cost of normal upgrades under the software maintenance
contracts MOC has with the software vendors. MOC is also in the process of
communicating with its significant suppliers, larger customers, and partners to
determine the extent to which it may be vulnerable to those third parties'
failure to remedy their Year 2000 issues.


                           Part II - Other Information

ITEM 6.     EXHIBITS AND REPORTS ON FORM 8-K

     (a)    Exhibits - 27 Financial Data Schedule

     (b)    Reports on Form 8-K - none





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                                   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.


                              MEWBOURNE ENERGY PARTNERS 98-A, L.P.

                                  By: Mewbourne Development Corporation
                                      Managing General Partner




Date: November 4, 1998            By: /s/ J. Roe Buckley
                                     -------------------------------------------
                                      J. Roe Buckley, Treasurer
                                      and Chief Financial Officer












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                                Index to Exhibits

<TABLE>
<CAPTION>


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