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, 1999

      [  ]        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>

<TABLE>
<CAPTION>

                         MAY DRILLING PARTNERSHIP 1984-1
                     STATEMENTS OF NET ASSETS IN LIQUIDATION
                                   (Unaudited)
                                 (In thousands)



                                                                                March 31,                December 31,
                                                                                   1999                      1998

ASSETS
<S>                                                                                <C>                       <C> 
Investment in May Limited Partnership 1984-1                                       $ 18                      $ 40
                                                                                    ===                       ===


NET ASSETS IN LIQUIDATION                                                          $ 18                      $ 40
                                                                                    ===                       ===
</TABLE>






NOTE: The statements of operations,  changes in net assets in  liquidation,  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  statements  of  net  assets  in
liquidation.  The May Limited Partnership 1984-1 changed its basis of accounting
from the going concern basis to the  liquidation  basis  effective  December 31,
1998 as described in Note 1 to the financial statements.


























           The accompanying note is an integral part of the financial
                                  statements.


<PAGE>

<TABLE>
<CAPTION>

                         MAY LIMITED PARTNERSHIP 1984-1
                     STATEMENTS OF NET ASSETS IN LIQUIDATION
                                   (Unaudited)
                                 (In thousands)



                                                                       March 31,              December 31,
                                                                          1999                    1998

ASSETS
<S>                                                                     <C>                    <C>     
    Cash and cash equivalents                                           $    126               $    140
    Accrued oil and gas sales                                                 28                     40
    Due from affiliate                                                         9                     19

OIL AND GAS PROPERTIES,
    At estimated net realizable value                                         61                     61
                                                                        --------               --------

TOTAL ASSETS                                                                 224                    260
                                                                         -------                -------

LIABILITIES
    Accounts payable and accrued liabilities                                   6                     11
    Deferred appreciated gain on oil and gas properties                       52                     52
                                                                        --------               --------

NET ASSETS IN LIQUIDATION                                               $    166               $    197
                                                                         =======                =======
</TABLE>






























           The accompanying note is an integral part of the financial
                                  statements.


<PAGE>

<TABLE>
<CAPTION>

                         MAY LIMITED PARTNERSHIP 1984-1
              STATEMENT OF CHANGES IN NET ASSETS IN LIQUIDATION FOR THE
                        THREE MONTHS ENDED MARCH 31, 1999
              STATEMENT OF OPERATIONS FOR THE THREE MONTHS ENDED MARCH 31, 1998
                                   (Unaudited)
                   (In thousands, except for unit information)



                                                                         1999                        1998
                                                                         ----                        ----

REVENUES
<S>                                                                  <C>                         <C>      
   Gas revenue                                                       $      30                   $      88
   Oil revenue                                                              17                          43
   Interest                                                                  1                           3
                                                                     ---------                   ---------
         Total                                                              48                         134
                                                                      --------                     -------

COSTS AND EXPENSES
   Lease operating                                                           3                           5
   Production taxes                                                          4                           9
   General and administrative                                                7                           7
   Depletion                                                                 2                           4
   Professional services and other                                           4                           5
                                                                     ---------                   ---------
         Total                                                              20                          30
                                                                      --------                    --------

NET INCOME FROM OPERATIONS                                                  28                    $    104
                                                                                                   =======

NET ASSETS BEGINNING OF PERIOD                                             197

DISTRIBUTIONS TO PARTNERS                                                  (59)

NET ASSETS IN LIQUIDATION,
   END OF PERIOD                                                      $    166
                                                                       =======

ALLOCATION OF NET INCOME:

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

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

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

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

</TABLE>









           The accompanying note is an integral part of the financial
                                  statements.


<PAGE>

<TABLE>
<CAPTION>

                         MAY LIMITED PARTNERSHIP 1984-1
                             STATEMENT OF CASH FLOWS
                    FOR THE THREE MONTHS ENDED MARCH 31, 1998
                                   (Unaudited)
                                 (In thousands)



OPERATING ACTIVITIES:
<S>                                                                                                <C>    
    Net income                                                                                     $   104
    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
      Due from affiliate                                                                                28
      Accounts payable and accrued liabilities                                                          (4)
                                                                                                  --------
              Net cash provided by operating activities                                                186
                                                                                                    ------

FINANCING ACTIVITIES -
      Distributions to partners                                                                       (191)

NET DECREASE IN CASH AND
    CASH EQUIVALENTS                                                                                    (5)

CASH AND CASH EQUIVALENTS:
       Balance, beginning of period                                                                    221

       Balance, end of period                                                                      $   216
                                                                                                    ======
</TABLE>

























           The accompanying note is an integral part of the financial
                                  statements.


<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, 1998 Annual Report on Form 10-K.

The terms of the partnership  agreements  governing the General  Partnership and
the Limited  Partnership  provide  for a fifteen  year term of  existence  which
extends through July 18, 1999. The partnerships are expected to be liquidated in
1999. As a result, the General  Partnership and the Limited  Partnership changed
their basis of accounting from the going concern basis to the liquidation  basis
effective December 31, 1998.  Accordingly,  assets have been valued at estimated
realizable value, net of estimated  disposition costs, and liabilities have been
adjusted to estimated settlement amounts, as follows (in thousands):
<TABLE>
<CAPTION>

                                                            March 31,       December 31,
                                                               1999              1998

<S>                                                            <C>              <C>   
Appreciation of oil and gas properties                         $   52           $   52
Deferral of appreciated gain on oil and gas properties            (52)             (52)
</TABLE>

The Company has received an appraisal indicating an appreciation of $52,000 over
the  historical  net  carrying  value of the Limited  Partnership's  oil and gas
properties  at March 31, 1999 and  December  31,  1998.  Because of the inherent
uncertainty  about the  timing  and  amount of the gain that may  ultimately  be
realized,  such  estimated gain has been deferred at March 31, 1999 and December
31, 1998.

Upon  completion of the liquidation  process and settlement of all  liabilities,
the  General  Partnership  will  distribute  the  remaining  cash to the General
Partnership  and  Limited  Partnership  in  accordance  with  the  terms  of the
partnership agreements.

The  statements of  operations,  and cash flows of the Limited  Partnership  for
three months ended March 31, 1998 have been prepared using the  historical  cost
(going  concern)  basis of accounting on which the General  Partnership  and the
Limited  Partnership  had  previously  reported  their  financial  condition and
results of operations.

After July 18,  1999,  the general  partner will proceed to wind-up the Drilling
Partnership and the Limited Partnership. This process includes preparing a final
accounting, paying the liabilities of the Partnerships, and making a liquidating
distribution  in  accordance  with the  capital  accounts of the  partners.  The
Limited Partnership owns a minority interest in one well. The general partner is
considering  the  alternatives  available for the liquidation of the partnership
and has not yet made a decision.




<PAGE>


ITEM 2    -  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
             RESULTS OF OPERATIONS
             
Liquidity and Capital Resources

The Partnership distributed $59,000 to partners during the first three months of
1999.  A  distribution  payable to  partners  of record as of March 31, 1999 was
declared in April 1999. The  distribution  amount is $86,000  payable $53,922 to
May Drilling Partnership 1984-1 partners and $32,078 to the general partner.

Issues Related to the Year 2000

Although the Limited  Partnership  will most likely be  liquidated  prior to the
Year  2000,  it is  continuing  to pursue  its Year 2000 Plan so that it will be
prepared, if necessary, to address Year 2000 problems.

General.  The following  Year 2000  statements  constitute a Year 2000 Readiness
Disclosure  within  the  meaning  of the Year  2000  Information  and  Readiness
Disclosure  Act of 1998.  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 Limited 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 Limited 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  Limited
Partnership  began  its phase  one  assessment  of its  particular  exposure  to
problems that might arise as a result of the new millennium.  The assessment and
inventory  plans  have  been  substantially  completed  and  have  assessed  and
identified  the Limited  Partnership IT systems that must be updated or replaced
in order to be Year 2000  compliant.  In  particular,  the software  used by the
Limited  Partnership  for  reservoir  engineering  must be updated or  replaced.
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 Limited  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  Limited
Partnership's  assessment  of the  readiness of third  parties  whose IT systems
might  have an impact on the  Limited  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 Limited Partnership's Non IT systems, the Limited Partnership
believes that most of these systems can be brought into  compliance on schedule.
The  Limited  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 Limited 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  Limited
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.



<PAGE>


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 Limited Partnership's
IT and Non IT systems, as well as to the systems of third parties. Such failures
could  materially  and  adversely  affect the Limited  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
Limited Partnership is unable to determine at this time whether the consequences
of Year 2000 failures will have a material  impact on the Limited  Partnership's
results of operations,  cash flow or financial  condition.  Although the Limited
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 Limited  Partnership.  The Limited  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 Limited  Partnership's Year 2000
Plan is expected to  significantly  reduce the  Limited  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  Limited
Partnership's development of contingency plans.

Cautionary Statement Regarding Forward-Looking Statements

In the interest of providing the partners with certain information regarding the
Limited 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  Limited  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  Limited  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 Limited
Partnership's  oil and gas operations,  the inexact nature of  interpretation of
seismic  and other  geological  and  geophysical  data,  imprecision  of reserve
estimates,  the Limited  Partnership's ability to replace and expand oil and gas
reserves, and such other risks and uncertainties  described from time to time in
the Limited  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 Limited 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 Limited 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

First Quarter 1999 Compared to First Quarter 1998

Gas Revenue

Gas revenue  decreased  $58,000 during the first quarter of 1999 compared to the
first quarter of 1998 due to a 57% 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 $2.59 per mcf in 1998 to $2.05 in 1999.

Oil Revenue

Oil  revenues  decreased  $26,000 in the first  quarter of 1999  compared to the
first quarter of 1998 as a result of a decrease in production  and a decrease in
the average oil price. Oil production  decreased 49% on the Freddie Aker #1 well
due to increased  rates of water  production on the well.  The average oil price
decreased from $14.63 per barrel in 1998 to $11.18 per barrel in 1999.



<PAGE>


Interest

Interest  income  decreased  $2,000 during the first quarter of 1999 compared to
the first quarter of 1998 due to a lower average cash balance during 1999.

Lease Operating

Lease  operating  expense  decreased  $2,000  during  the first  quarter of 1999
compared to the first quarter of 1998 due to decreased  maintenance  activity on
the Freddie Aker #1 well.

Production Taxes

Production  taxes decreased  $5,000 during the first quarter of 1999 compared to
the first quarter of 1998 due to decreased production previously discussed.

Depletion

Depletion  expense decreased $2,000 during the first quarter of 1999 compared to
the first quarter of 1998 due to a decrease in the depletion rate resulting from
lower production during 1999.

Professional Services and Other

Professional  services  and other  expense  decreased  $1,000  during  the first
quarter of 1999  compared  to the first  quarter  of 1998 due to a  decrease  in
numerous miscellaneous items, none of which is individually significant.


<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, 1998.


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 11, 1999                            By:  /s/Thomas J. Jung
                                                Thomas J. Jung, Vice President
                                                 (Principal Accounting Officer)