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 June 30, 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 10


<PAGE>

<TABLE>
<CAPTION>


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



                                                                               June 30,                 December 31,
                                                                                  1998                      1997

ASSETS
<S>                                                                              <C>                       <C>  
Investment in May Limited Partnership 1984-1                                     $  77                     $ 188


PARTNERS' CAPITAL
Partners' Capital                                                                $  77                     $ 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)



                                                                      June 30,              December 31,
                                                                        1998                    1997

ASSETS
CURRENT ASSETS
<S>                                                                    <C>                     <C>    
    Cash and cash equivalents                                          $   163                 $   221
    Accrued oil and gas sales                                               52                     127
    Due from affiliate                                                      31                      70
         Total                                                             246                     418

OIL AND GAS PROPERTIES, using the
    full cost method of accounting                                       8,112                   8,112
       Less accumulated depletion                                      ( 8,097)                  (8,091)
         Net oil and gas properties                                         15                      21

TOTAL ASSETS                                                           $   261                 $   439

LIABILITIES AND PARTNERS' CAPITAL
CURRENT LIABILITIES
    Accounts payable and accrued liabilities                         $       7                $     12

PARTNERS' CAPITAL
    General partner                                                        177                     239
    Limited partner                                                         77                     188
         Total                                                             254                     427

TOTAL LIABILITIES AND PARTNERS' CAPITAL                                $   261                 $   439




















<FN>

</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 June 30,
                                                                        1998                      1997

REVENUES
<S>                                                                  <C>                        <C>     
   Gas revenue                                                       $     63                   $     94
   Oil revenue                                                             31                         65
   Interest                                                                 3                          3
    Other                                                                                              6
         Total                                                             97                        168

COSTS AND EXPENSES
   Lease operating                                                          7                          8
   Production taxes                                                         7                         12
   General and administrative                                               7                          7
   Depletion                                                                2                          9
   Professional services and other                                          2                          2
         Total                                                             25                         38

NET INCOME                                                           $     72                    $   130

ALLOCATION OF NET INCOME:

    General Partner                                                  $     29                   $     50

    Limited Partner                                                  $     43                   $     80

       Per initial $1,000 limited partner
         investment                                                   $  8.01                     $14.89

       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 OPERATIONS
                                   (Unaudited)
                   (In thousands, except for unit information)



                                                                       For the Six Months Ended June 30,
                                                                        1998                      1997

REVENUES
<S>                                                                   <C>                        <C>    
   Gas revenue                                                        $   151                    $   261
   Oil revenue                                                             74                        169
   Interest                                                                 6                          6
   Other                                                                                               6
         Total                                                            231                        442

COSTS AND EXPENSES
   Lease operating                                                         12                         16
   Production taxes                                                        16                         29
   General and administrative                                              14                         14
   Depletion                                                                6                          9
   Professional services and other                                          7                          7
         Total                                                             55                         75

NET INCOME                                                            $   176                    $   367

ALLOCATION OF NET INCOME:

    General Partner                                                  $     68                    $   141

    Limited Partner                                                   $   108                    $   226

       Per initial $1,000 limited partner
         investment                                                    $20.11                     $42.08

       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 Six Months Ended June 30,
                                                                         1998                      1997

OPERATING ACTIVITIES:
<S>                                                                   <C>                       <C>     
    Net income                                                        $    176                  $    367
    Adjustment to reconcile net income to net
       cash provided by operating activities:
          Depletion                                                          6                         9

Changes in assets and liabilities provided (used) cash:
      Accrued oil and gas sales                                             75                        94
      Due from affiliate                                                    39                        75
      Accounts payable and accrued liabilities                              (5)                       (5)
      Due to affiliate                                                                                18
              Net cash provided by operating activities                    291                       558

INVESTING ACTIVITIES -
      Additions to oil and gas properties                                                            (44)

FINANCING ACTIVITIES -
      Distributions to partners                                           (349)                     (551)

NET DECREASE IN CASH AND
    CASH EQUIVALENTS                                                       (58)                      (37)

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

       Balance, end of period                                          $   163                   $   228


















<FN>

</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 $291,000 for the six months ended
June 30, 1998, and $349,000 was distributed to partners.  A distribution payable
to  partners  of record  as of June 30,  1998 was  declared  in July  1998.  The
distribution  amount is  $94,000  payable  $58,938 to May  Drilling  Partnership
1984-1 partners and $35,062 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

Second Quarter 1998 Compared to Second Quarter 1997

Gas Revenue

Gas revenue  decreased  $31,000 during the second quarter of 1998 as compared to
the second quarter of 1997 due to a 36% decrease in production, partially offset
by an increase in the average gas price.  The decrease in  production  is due to
increased  rates of water  production  on the Freddie Aker #1 well in Louisiana.
The average gas price increased from $2.49 per mcf in 1997 to $2.66 in 1998.

Oil Revenue

Oil revenues  decreased $34,000 in the second quarter of 1998 as compared to the
second quarter of 1997 as a result of a decrease in production and a decrease in
the average oil price. Oil production  decreased 31% on the Freddie Aker #1 well
due to increased  rates of water  production on the well.  The average oil price
decreased from $19.38 per barrel in 1997 to $13.19 per barrel in 1998.

Other

Other income during 1997 is comprised of insurance  proceeds which  reimbursed a
portion of expense incurred in a prior period to settle certain litigation.

Lease Operating

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


<PAGE>


Production Taxes

Production  taxes decreased $5,000 during the second quarter of 1998 as compared
to the second quarter of 1997 due to decreased production previously discussed.

Depletion

Depletion expense decreased $7,000 during the second quarter of 1998 as compared
to the second  quarter of 1997 due to a decrease in the depletion rate resulting
from lower production during 1998.

Six Months Ended June 30, 1998 Compared to the Six Months Ended June 30, 1997

The  comparisons for the six months ended June 30, 1998 and the six months ended
June 30, 1997 are  consistent  with those  discussed in the second  quarter 1998
compared to the second quarter of 1997 except for the following:

Gas Revenue

Gas revenue  decreased  $110,000 during the first six months of 1998 as compared
to the  corresponding  period  in 1997 due to a  decrease  in  production  and a
decrease in price. Gas production  decreased 33% due to increased rates of water
production  on the Freddie Aker #1 well.  The average gas price  decreased  from
$3.03 per mcf in 1997 to $2.62 per mcf in 1998.

Oil Revenue

Oil revenue decreased $95,000 during the first six months of 1998 as compared to
the corresponding  period in 1997 due to a decrease in production and a decrease
in the average oil price. The average oil price decreased from $21.28 per barrel
in 1997 to  $14.00  per  barrel in 1998.  Oil  production  decreased  33% due to
increased rates of water production on the Freddie Aker #1 well.


<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:  August 10, 1998                By: /s/Thomas J. Jung
                                          Thomas J. Jung, Vice President
                                          (Principal Accounting Officer)