UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D. C. 20549

                                    Form 10-Q

MARK ONE
      [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

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

                         Commission File Number 2-89194


                         MAY DRILLING PARTNERSHIP 1984-1
                         MAY LIMITED PARTNERSHIP 1984-1
             (Exact name of registrant as specified in its charter)


                                                                      75-1973664
               Texas                                                  75-1973661
    (State or other jurisdiction of                             (I.R.S. Employer
    incorporation or organization)                        Identification Number)

    4582 South Ulster Street Parkway
               Suite 1700
            Denver, Colorado                                               80237
    (Address of principal executive offices)                          (Zip Code)

       Registrant's telephone number, including area code: (303) 850-7373

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 [ ]












                                   Page 1 of 9


<PAGE>


<TABLE>
<CAPTION>

                         MAY DRILLING PARTNERSHIP 1984-1
                                 BALANCE SHEETS
                                   (Unaudited)
                                 (In thousands)



                                                                               March 31,                December 31,
                                                                                  1998                      1997

ASSETS
<S>                                                                              <C>                       <C>  
Investment in May Limited Partnership 1984-1                                     $ 133                     $ 188
                                                                                  ====                      ====


PARTNERS' CAPITAL
Partners' Capital                                                                $ 133                     $ 188
                                                                                  ====                      ====




<FN>


NOTE:      The  statements  of  operations  and  cash  flows  for  May  Drilling
           Partnership  1984-1 are not  presented  because such  information  is
           equal to the limited partner's share of such activity as presented in
           the May Limited  Partnership  1984-1  financial  statements.  The May
           Drilling   Partnership   carries  its   investment   in  May  Limited
           Partnership 1984-1 on the equity method. The May Limited  Partnership
           1984-1 financial  statements should be read in conjunction with these
           balance sheets.
</FN>

























<FN>

           The accompanying note is an integral part of the financial
                                  statements.
</FN>
</TABLE>


<PAGE>

<TABLE>
<CAPTION>

                         MAY LIMITED PARTNERSHIP 1984-1
                                 BALANCE SHEETS
                                   (Unaudited)
                                 (In thousands)



                                                                     March 31,              December 31,
                                                                        1998                    1997

ASSETS
CURRENT ASSETS
<S>                                                                    <C>                     <C>    
    Cash and cash equivalents                                          $   216                 $   221
    Accrued oil and gas sales                                               73                     127
    Due from affiliate                                                      42                      70
                                                                       -------                 -------
         Total                                                             331                     418
                                                                        ------                  ------

OIL AND GAS PROPERTIES, using the
    full cost method of accounting                                       8,112                   8,112
       Less accumulated depletion                                       (8,095)                  (8,091)
                                                                         -----                    -----
         Net oil and gas properties                                         17                      21
                                                                       -------                 -------

TOTAL ASSETS                                                           $   348                 $   439
                                                                        ======                  ======

LIABILITIES AND PARTNERS' CAPITAL
CURRENT LIABILITIES
    Accounts payable and accrued liabilities                         $       8                $     12
                                                                      --------                 -------

PARTNERS' CAPITAL
    General partner                                                         207                    239
    Limited partner                                                         133                    188
                                                                         ------                 ------
         Total                                                              340                    427
                                                                         ------                 ------

TOTAL LIABILITIES AND PARTNERS' CAPITAL                                 $   348                $   439
                                                                         ======                 ======




















<FN>

           The accompanying note is an integral part of the financial
                                  statements.
</FN>
</TABLE>


<PAGE>

<TABLE>
<CAPTION>

                         MAY LIMITED PARTNERSHIP 1984-1
                            STATEMENTS OF OPERATIONS
                                   (Unaudited)
                   (In thousands, except for unit information)



                                                                      For the Three Months Ended March 31,
                                                                        1998                      1997

REVENUES
<S>                                                                   <C>                        <C>    
    Oil revenue                                                       $    43                    $   104
    Gas revenue                                                            88                        167
    Interest                                                                3                          3
                                                                     --------                   --------
         Total                                                            134                        274
                                                                       ------                     ------

COSTS AND EXPENSES
   Lease operating                                                          5                          8
   Production taxes                                                         9                         17
   General and administrative                                               7                          7
   Depletion                                                                4
   Professional services and other                                          5                          5
                                                                     --------                   --------
         Total                                                             30                         37
                                                                      -------                    -------

NET INCOME                                                            $   104                    $   237
                                                                       ======                     ======

ALLOCATION OF NET INCOME:

    General Partner                                                  $     39                   $     91
                                                                      =======                    =======

    Limited Partner                                                  $     65                    $   146
                                                                      =======                     ======

       Per initial $1,000 limited partner
         investment                                                    $12.10                     $27.18
                                                                        =====                      =====

       Weighted average initial $1,000 limited
         partner investment units outstanding                           5,371                      5,371
                                                                       ======                     ======

















<FN>

           The accompanying note is an integral part of the financial
                                  statements.
</FN>
</TABLE>


<PAGE>

<TABLE>
<CAPTION>

                         MAY LIMITED PARTNERSHIP 1984-1
                            STATEMENTS OF CASH FLOWS
                                   (Unaudited)
                                 (In thousands)



                                                                      For the Three Months Ended March 31,
                                                                         1998                      1997

OPERATING ACTIVITIES:
<S>                                                                    <C>                       <C>    
    Net income                                                         $   104                   $   237
    Adjustment to reconcile net income to net
       cash provided by operating activities:
          Depletion                                                          4

Changes in assets and liabilities provided (used) cash:
      Accrued oil and gas sales                                             54                        77
      Due from affiliate                                                    28                       (36)
      Accounts payable and accrued liabilities                              (4)                       (4)
                                                                      --------                  --------
              Net cash provided by operating activities                    186                       274
                                                                        ------                    ------

INVESTING ACTIVITIES -
      Additions to oil and gas properties                                                           (242)
                                                                     ---------                    ------

FINANCING ACTIVITIES -
      Distributions to partners                                           (191)

NET INCREASE (DECREASE) IN CASH AND
    CASH EQUIVALENTS                                                        (5)                       32

CASH AND CASH EQUIVALENTS:
       Balance, beginning of period                                        221                       265
                                                                        ------                    ------

       Balance, end of period                                          $   216                   $   297
                                                                        ======                    ======



















<FN>

           The accompanying note is an integral part of the financial
                                  statements.
</FN>
</TABLE>


<PAGE>


                         MAY LIMITED PARTNERSHIP 1984-1
                          NOTE TO FINANCIAL STATEMENTS
                                   (Unaudited)



NOTE 1    -   GENERAL

The financial  statements  presented are those of May Limited Partnership 1984-1
(the "Partnership").  The interim financial data are unaudited;  however, in the
opinion of the general  partner,  the  interim  data  include  all  adjustments,
consisting  only  of  normal  recurring   adjustments,   necessary  for  a  fair
presentation of the results for the interim periods.  These financial statements
should be read in  conjunction  with the financial  statements and notes thereto
included in the Partnership's December 31, 1997 Annual Report on Form 10-K.


ITEM 2    -  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
             RESULTS OF OPERATIONS


Liquidity and Capital Resources

Cash  provided by  operating  activities  totaled  $186,000 for the three months
ended March 31, 1998, and $191,000 was  distributed to partners.  A distribution
payable to partners  of record as of March 31, 1998 was  declared in April 1998.
The distribution amount is $158,000 payable $99,066 to May Drilling  Partnership
1984-1 partners and $58,934 to the general  partner.  Future  distributions  are
dependent on future prices for the  Partnership's  production and the production
level of the Partnership's remaining oil and gas reserves.

Results of Operations

First Quarter 1998 Compared to First Quarter 1997

Oil Revenue

Oil revenues decreased $61,000 in the first quarter of 1998 as compared with the
first quarter of 1997 as a result of a decrease in production  and a decrease in
the average oil price.  Oil production  decreased 35% on the Freddie Aker #1 due
to  increased  rates of water  production  on the well.  The  average  oil price
decreased from $22.68 per barrel in 1997 to $14.63 per barrel in 1998.

Gas Revenue

Gas revenue  decreased  $79,000  during the first quarter of 1998 as compared to
the first quarter of 1997 due to a 30% decrease in production  and a decrease in
the average gas price.  The decrease in production is due to increased  rates of
water  production on the Freddie Aker #1. The average gas price  decreased  from
$3.45 per mcf in 1997 to $2.59 in 1998.

Lease Operating

Lease  operating  expense  decreased  $3,000 during the first quarter of 1998 as
compared to the first quarter of 1997 due to decreased  maintenance  activity on
the Freddie Aker #1 well.

Production Taxes

Production  taxes decreased  $8,000 during the first quarter of 1998 as compared
to the first quarter of 1997 due to decreased production previously discussed.


<PAGE>


Depletion

Depletion  expense increased $4,000 during the first quarter of 1998 as compared
with the first quarter of 1997 due to increased capital costs during 1998.


<PAGE>


 PART II - OTHER INFORMATION


ITEM 1 -     LEGAL PROCEEDINGS

             Reference  is made to Item 8 - Note 4 of  Form  10-K  for the  year
             ended December 31, 1997.


ITEM 2 -     CHANGES IN SECURITIES

             None.


ITEM 3 -     DEFAULTS UPON SENIOR SECURITIES

             None.


ITEM 4 -     SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS
             

             None.


ITEM 5 -     OTHER INFORMATION

             None.


ITEM 6 -     EXHIBITS AND REPORTS ON FORM 8-K

             None.



<PAGE>


SIGNATURE

Pursuant  to the  requirements  of the  Securities  Exchange  Act of  1934,  the
Partnerships  have duly caused  this report to be signed on their  behalf by the
undersigned, thereunto duly authorized.

                                    MAY DRILLING PARTNERSHIP 1984-1
                                    MAY LIMITED PARTNERSHIP 1984-1

                                    By:  EDP OPERATING, LTD.,
                                         General Partner

                                         By:  HEPGP Ltd.,
                                              General Partner

                                         By:  HALLWOOD G. P., INC.,
                                              General Partner



Date:  May 1, 1998                       By:  /s/Thomas J. Jung
------------------                           -------------------------------
                                              Thomas J. Jung, Vice President
                                              (Principal Accounting Officer)