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 September 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 11


<PAGE>
<TABLE>
<CAPTION>


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



                                                                              September 30,              December 31,
                                                                                   1998                      1997

ASSETS
<S>                                                                               <C>                       <C>  
Investment in May Limited Partnership 1984-1                                      $  56                     $ 188
                                                                                   ====                      ====


PARTNERS' CAPITAL
Partners' Capital                                                                 $  56                     $ 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)



                                                                     September 30,            December 31,
                                                                          1998                    1997

ASSETS
CURRENT ASSETS
<S>                                                                     <C>                    <C>     
    Cash and cash equivalents                                           $    146               $    221
    Accrued oil and gas sales                                                 44                    127
    Due from affiliate                                                        27                     70
                                                                        --------               --------
         Total                                                               217                    418
                                                                         -------                -------

OIL AND GAS PROPERTIES, using the
    full cost method of accounting                                         8,112                  8,112
       Less accumulated depletion                                         (8,100)                 (8,091)
                                                                           -----                   -----
         Net oil and gas properties                                           12                     21
                                                                        --------               --------

TOTAL ASSETS                                                            $    229               $    439
                                                                         =======                =======

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

PARTNERS' CAPITAL
    General partner                                                          165                    239
    Limited partner                                                           56                    188
                                                                        --------                -------
         Total                                                               221                    427
                                                                         -------                -------

TOTAL LIABILITIES AND PARTNERS' CAPITAL                                 $    229               $    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 September 30,
                                                                         1998                       1997

REVENUES
<S>                                                                    <C>                        <C>     
   Gas revenue                                                         $    54                    $    122
   Oil revenue                                                              28                          83
   Interest                                                                  3                           3
    Other                                                                                      
                                                                   -----------
         Total                                                              85                         208
                                                                      --------                     -------

COSTS AND EXPENSES
   Lease operating                                                           5                           6
   Production taxes                                                          6                          14
   General and administrative                                                8                           8
   Depletion                                                                 3                          12
   Professional services and other                                           2                           2
                                                                    ----------                  ----------
         Total                                                              24                          42
                                                                     ---------                   ---------

NET INCOME                                                          $       61                    $    166
                                                                     =========                     =======

ALLOCATION OF NET INCOME:

    General Partner                                                 $       23                   $      64
                                                                     =========                    ========

    Limited Partner                                                 $       38                    $    102
                                                                     =========                     =======

       Per initial $1,000 limited partner
         investment                                                   $   7.08                     $ 18.99
                                                                       =======                      ======

       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 Nine Months Ended September 30,
                                                                         1998                       1997

REVENUES
<S>                                                                    <C>                         <C>    
   Gas revenue                                                         $   205                     $   383
   Oil revenue                                                             102                         252
   Interest                                                                  9                           9
   Other                                                                                                 6
                                                                     ---------                    --------
         Total                                                             316                         650
                                                                        ------                      ------

COSTS AND EXPENSES
   Lease operating                                                          17                          22
   Production taxes                                                         22                          43
   General and administrative                                               22                          22
   Depletion                                                                 9                          21
   Professional services and other                                           9                           9
                                                                      --------                    --------
         Total                                                              79                         117
                                                                       -------                      ------

NET INCOME                                                             $   237                     $   533
                                                                        ======                      ======

ALLOCATION OF NET INCOME:

    General Partner                                                   $     91                     $   205
                                                                       =======                      ======

    Limited Partner                                                    $   146                     $   328
                                                                        ======                      ======

       Per initial $1,000 limited partner
         investment                                                     $27.18                      $61.07
                                                                         =====                       =====

       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 Nine Months Ended September 30,
                                                                          1998                      1997

OPERATING ACTIVITIES:
<S>                                                                     <C>                        <C>    
    Net income                                                          $   237                    $   533
    Adjustment to reconcile net income to net
       cash provided by operating activities:
          Depletion                                                           9                         21

Changes in assets and liabilities provided (used) cash:
      Accrued oil and gas sales                                              83                         83
      Due from affiliate                                                     43                         12
      Accounts payable and accrued liabilities                               (4)                        (1)
                                                                       --------                   --------
              Net cash provided by operating activities                     368                        648
                                                                         ------                     ------

INVESTING ACTIVITIES -
      Additions to oil and gas properties                                                              (47)
                                                                      ---------                    -------

FINANCING ACTIVITIES -
      Distributions to partners                                            (443)                      (662)
                                                                         ------                     ------

NET DECREASE IN CASH AND
    CASH EQUIVALENTS                                                        (75)                       (61)

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

       Balance, end of period                                           $   146                    $   204
                                                                         ======                     ======


















<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 $368,000 for the nine months ended
September 30, 1998,  and $443,000 was  distributed  to partners.  A distribution
payable to partners of record as of  September  30, 1998 was declared in October
1998.  The  distribution  amount is  $73,000  payable  $45,771  to May  Drilling
Partnership  1984-1  partners  and  $27,229  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.

Year 2000 Update

General.  The Year 2000  problem  has  arisen  because  many  existing  computer
programs  use  only the last two  digits  to refer to a year.  Therefore,  these
computer  programs  do  not  properly   recognize  and  process  date  sensitive
information  beyond  1999.  In  general,  there  are two areas  where  Year 2000
problems  may  exist  for  the  Partnership:   information  technology  such  as
computers,  programs and related systems ("IT") and  non-information  technology
systems such as embedded technology on a silicon chip ("Non IT").

The Plan.  The  Partnership's  Year 2000 Plan (the "Plan") has four phases:  (i)
assessment,  (ii) inventory,  (iii) remediation,  testing and implementation and
(iv) contingency plans.  Approximately  twelve months ago, the Partnership began
its phase one assessment of its particular exposure to problems that might arise
as a result of the new millennium.  The assessment phase has been  substantially
completed and has identified the  Partnership IT systems that must be updated or
replaced in order to be Year 2000 compliant. In particular, the software used by
the  Partnership  for  reservoir  engineering  must be updated or replaced.  The
inventory  phase  of the  Plan  is  currently  underway  and is  expected  to be
completed by December  31, 1998.  Remediation,  testing and  implementation  are
scheduled to be completed by June 30, 1999, and the  contingency  plans phase of
the Plan is scheduled to be completed by September 30, 1999.

To date, the Partnership has determined that its IT systems are either compliant
or can be made compliant without material cost. However, the effects of the Year
2000 problem on IT systems are  exacerbated  because of the  interdependence  of
computer  systems in the United  States.  The  Partnership's  assessment  of the
readiness  of third  parties  whose  IT  systems  might  have an  impact  on the
Partnership's  business has thus far not  indicated any material  problems;  the
process of inquiring of third parties and reviewing  their responses is underway
but is not complete.

With regard to the Partnership's Non IT systems,  the Partnership  believes that
most  of  these  systems  can  be  brought  into  compliance  on  schedule.  The
Partnership's assessment of third party readiness is not yet completed.  Because
Non IT systems are embedded  chips,  it is difficult to determine  with complete
accuracy  where  all  such  systems  are  located.  As  part  of its  Plan,  the
Partnership  is making formal and informal  inquiries of its vendors,  customers
and  transporters  in an effort to determine  the third party systems that might
have embedded technology requiring remediation.  Estimated Costs. Although it is
difficult to estimate the total costs of  implementing  the Plan through January
1, 2000 and beyond,  the Partnership's  preliminary  estimate is that such costs
will not be material.  However,  although management believes that its estimates
are  reasonable,  there can be no assurance,  for the reasons stated in the next
paragraph,  that  the  actual  cost of  implementing  the Plan  will not  differ
materially from the estimated costs.

Potential  Risks.  The  failure to correct a material  Year 2000  problem  could
result  in  an  interruption  in,  or a  failure  of,  certain  normal  business
activities or operations.  This risk exists both as to the  Partnership's IT and
Non IT systems, as well as to the systems of third parties.  Such failures could
materially and adversely affect the  Partnership's  results of operations,  cash
flow and financial  condition.  Due to the general  uncertainty  inherent in the
Year  2000  problem,  resulting  in part from the  uncertainty  of the Year 2000
readiness of third party suppliers, vendors and transporters, the Partnership is
unable to determine at this time whether the  consequences of Year 2000 failures
will have a material  impact on the  Partnership's  results of operations,  cash
flow or financial  condition.  Although the Partnership is not currently able to
determine the consequences of Year 2000 failures, its current assessment is that
its area of greatest  potential risk is in connection with the  transporting and
marketing of the oil and gas produced by the  Partnership.  The  Partnership  is
contacting  the various  purchasers  and pipelines  with which it regularly does
business  to  determine  their  state  of  readiness  for  the  Year  2000.  The
Partnership's   Year  2000  Plan  is  expected  to   significantly   reduce  the
Partnership's  level of uncertainty  about the compliance and readiness of these
material third parties. The evaluation of third party readiness will be followed
by the Partnership's development of contingency plans.

Cautionary Statement Regarding Forward-Looking Statements

In the interest of providing the partners with certain information regarding the
Partnership's future plans and operations,  certain statements set forth in this
Form 10-Q relate to management's  future plans and  objectives.  Such statements
are  forward-looking   statements.   Although  any  forward-looking   statements
contained  in this  Form  10-Q or  otherwise  expressed  by or on  behalf of the
Partnership  are,  to the  knowledge  and in the  judgment of the  officers  and
directors  of the  general  partner,  expected  to prove  true and come to pass,
management  is  not  able  to  predict  the  future  with  absolute   certainty.
Forward-looking  statements  involve known and unknown  risks and  uncertainties
which may cause the  Partnership's  actual  performance and financial results in
future periods to differ materially from any projection,  estimate or forecasted
result. These risks and uncertainties include, among other things, volatility of
oil and gas prices, competition, risks inherent in the Partnership's oil and gas
operations, the inexact nature of interpretation of seismic and other geological
and  geophysical  data,  imprecision  of reserve  estimates,  the  Partnership's
ability to replace  and expand oil and gas  reserves,  and such other  risks and
uncertainties  described from time to time in the Partnership's periodic reports
and filings with the Securities and Exchange Commission.  In addition, the dates
for  completion  of  the  phases  of  the  Year  2000  Plan  are  based  on  the
Partnership's best estimates,  which were derived using numerous  assumptions of
future events. Due to the general uncertainty inherent in the Year 2000 problem,
resulting  in  part  from  the   uncertainty  of  the  Year  2000  readiness  of
third-parties  and the  interconnection  of computer  systems,  the  Partnership
cannot  ensure  its  ability  to timely and  cost-effectively  resolve  problems
associated with the Year 2000 issue that may affect its operations and business.
Accordingly,  partners are cautioned that certain events or circumstances  could
cause actual results to differ  materially  from those  projected,  estimated or
predicted.

Results of Operations

Third Quarter 1998 Compared to Third Quarter 1997

Gas Revenue

Gas revenue  decreased  $68,000 during the third quarter of 1998 compared to the
third quarter of 1997 due to a 47% 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 well in  Louisiana.  The  average gas price
decreased from $2.71 per mcf in 1997 to $2.27 in 1998.


<PAGE>


Oil Revenue

Oil  revenues  decreased  $55,000 in the third  quarter of 1998  compared to the
third quarter of 1997 as a result of a decrease in production  and a decrease in
the average oil price. Oil production  decreased 47% on the Freddie Aker #1 well
due to increased  rates of water  production on the well.  The average oil price
decreased from $19.24 per barrel in 1997 to $12.21 per barrel in 1998.

Lease Operating

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

Production Taxes

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

Depletion

Depletion  expense decreased $9,000 during the third quarter of 1998 compared to
the third quarter of 1997 due to a decrease in the depletion rate resulting from
lower production during 1998.

Nine Months Ended September 30, 1998 Compared to the Nine Months Ended September
30, 1997

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

Gas Revenue

Gas revenue decreased  $178,000 during the first nine months of 1998 compared to
the corresponding  period in 1997 due to a decrease in production and a decrease
in  price.  Gas  production  decreased  38%  due to  increased  rates  of  water
production  on the Freddie Aker #1 well.  The average gas price  decreased  from
$2.92 per mcf in 1997 to $2.52 per mcf in 1998.

Oil Revenue

Oil revenue decreased  $150,000 during the first nine months of 1998 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 $20.56 per barrel
in 1997 to  $13.46  per  barrel in 1998.  Oil  production  decreased  38% due to
increased rates of water production on the Freddie Aker #1 well.

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.


<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:  November 9, 1998                    By: /s/Thomas J. Jung
                                               Thomas J. Jung, Vice President
                                               (Principal Accounting Officer)