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, 1996

   |_|                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)



                                                                               September 30,               December 31,
                                                                                   1996                        1995
ASSETS
Investment in
<S>                                                                                <C>                         <C>
     May Limited Partnership 1984-1                                                $247                        $177
                                                                                    ===                         ===

PARTNERS' CAPITAL
Partners' Capital                                                                  $247                        $177
                                                                                    ===                         ===






<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>

                                                        -2-

<PAGE>

<TABLE>
<CAPTION>


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


                                                                             September 30,                December 31,
                                                                               1996                        1995

ASSETS

CURRENT ASSETS
<S>                                                                               <C>                         <C>
     Cash and cash equivalents                                                    $    256                    $    197
     Accrued oil and gas sales                                                         163                         162
     Due from affiliate                                                                 99                          49
                                                                                  --------                    --------

              Total                                                                    518                         408
                                                                                   -------                     -------

OIL AND GAS PROPERTIES, using the
     full cost method of accounting                                                  8,064                       8,057
         Less - Accumulated depletion                                              (8,064)                     (8,057)
                                                                                   ------                      ------
              Net oil and gas properties                                                 -                           -
                                                                                ----------                   ---------

TOTAL ASSETS                                                                      $    518                     $   408
                                                                                   =======                      ======


LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES
     Accounts payable and accrued liabilities                                   $        9                    $     15
                                                                                 ---------                     -------

              Total                                                                      9                          15
                                                                                 ---------                     -------

PARTNERS' CAPITAL
     General partner                                                                   262                         216
     Limited partner                                                                   247                         177
                                                                                   -------                      ------

              Total                                                                    509                         393
                                                                                   -------                      ------

TOTAL LIABILITIES AND PARTNERS' CAPITAL                                           $    518                     $   408
                                                                                   =======                      ======









<FN>

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

                                                        -3-

<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,
                                                                                ---------------------------------
                                                                                 1996                         1995
                                                                            --------------                --------

REVENUES
<S>                                                                                <C>                        <C>
     Oil revenue                                                                   $   129                    $     89
     Gas revenue                                                                       170                         103
     Interest income                                                                     2                           2
                                                                                  --------                    --------
              Total                                                                    301                         194
                                                                                    ------                     -------

COSTS AND EXPENSES
     Lease operating                                                                     4                           4
     Production taxes                                                                   21                          16
     General and administrative                                                          7                          10
     Depletion                                                                           7
     Professional services and other                                                     2                           2
                                                                                  --------                    --------
              Total                                                                     41                          32
                                                                                   -------                     -------

NET INCOME                                                                         $   260                    $    162
                                                                                    ======                     =======

ALLOCATION OF NET INCOME:

     General Partner                                                              $     98                   $      60
                                                                                   =======                    ========

     Limited Partner                                                               $   162                     $   102
                                                                                    ======                      ======

         Per initial $1,000 limited partner investment                              $30.16                      $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>

                                                        -4-

<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,
                                                                              ---------------------------------
                                                                                 1996                         1995
                                                                            --------------                --------

REVENUES
<S>                                                                              <C>                         <C>
     Oil revenue                                                                 $     370                   $     253
     Gas revenue                                                                       626                         281
     Interest income                                                                     8                           8
                                                                                ----------                  ----------
              Total                                                                  1,004                         542
                                                                                   -------                    --------

COSTS AND EXPENSES
     Lease operating                                                                    14                          14
     Production taxes                                                                   63                          43
     General and administrative                                                         28                          32
     Depletion                                                                           7                           1
     Professional services and other                                                     7                           7
                                                                                ----------                  ----------
              Total                                                                    119                          97
                                                                                  --------                   ---------

NET INCOME                                                                       $     885                   $     445
                                                                                  ========                    ========

ALLOCATION OF NET INCOME:

     General Partner                                                             $     331                   $     167
                                                                                  ========                    ========

     Limited Partner                                                             $     554                   $     278
                                                                                  ========                    ========

         Per initial $1,000 limited partner investment                             $103.15                    $  51.76
                                                                                    ======                     =======

         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>

                                                        -5-

<PAGE>
<TABLE>
<CAPTION>



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



                                                                              For the Nine Months Ended
                                                                                    September 30,
                                                                          1996                        1995

OPERATING ACTIVITIES:
<S>                                                                              <C>                          <C>
     Net income                                                                  $     885                    $    445
     Adjustment to reconcile net income to
         net cash provided by operating activities:
              Depletion                                                                  7                           1
                                                                                ----------                   ---------

                  Cash from operations before working
                      capital changes                                                  892                         446

     Changes in assets and liabilities provided (used) cash:
              Accrued oil and gas sales                                                (1)                          22
              Due from affiliate                                                      (50)                           5
              Accounts payable and accrued liabilities                                 (6)                         (2)
                                                                                ---------                   ---------

                  Net cash provided by operating activities                            835                         471
                                                                                  --------                     -------

INVESTING ACTIVITIES:
     Additions to oil and gas properties                                               (7)                         (1)
                                                                                ---------                   ---------

                  Net cash used in investing activities                                (7)                         (1)
                                                                                ---------                   ---------

FINANCING ACTIVITIES:
     Distributions to partners                                                       (769)                       (457)
                                                                                  -------                     -------

                  Net cash used in financing activities                              (769)                       (457)
                                                                                  -------                     -------

NET INCREASE IN CASH AND
     CASH EQUIVALENTS                                                                   59                          13

CASH AND CASH EQUIVALENTS:
     Balance, beginning of period                                                      197                         217
                                                                                  --------                     -------

     Balance, end of period                                                      $     256                    $    230
                                                                                  ========                     =======


<FN>


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

                                                        -6-

<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, 1995 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 $835,000 for the nine months ended
September 30, 1996 and $769,000 was distributed to partners.  A distribution was
declared in October 1996. The distribution amount is $257,000,  payable $162,000
to May Drilling  Partnership 1984-1 partners and $95,000 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

Third Quarter 1996 Compared to the Third Quarter 1995

Oil Revenue

Oil revenue  increased  $40,000  during the third quarter of 1996 as compared to
the  corresponding  period in 1995 as the result of an  increase  in  production
combined with an increase in the average oil price. Oil production increased 13%
on the  Freddie  Aker #1 due to an increase  in the state  allowable  production
limits. The average oil price increased from $17.01 per barrel in 1995 to $21.86
per barrel in 1996.

Gas Revenue

Gas revenue  increased  $67,000  during the third quarter of 1996 as compared to
the  corresponding  period in 1995 due to an  increase  in the average gas price
combined  with an 8%  increase  in  production  due to an  increase in the state
allowable  production limits. The average gas price increased from $1.77 per mcf
in 1995 to $2.70 per mcf in 1996.

Production Taxes

Production  taxes increased  $5,000 during the third quarter of 1996 as compared
to the  corresponding  period  in 1995 due to  increased  production  previously
discussed.

General and Administrative

General and administrative  expense decreased $3,000 during the third quarter of
1996 as compared with the third quarter of 1995 as a result of a decrease in the
allocation of overhead from the general partner.


                                                        -7-

<PAGE>



Depletion

Depletion  expense increased $7,000 during the third quarter of 1996 as compared
with the third  quarter of 1995 due to an increase in  capitalized  costs during
1996.

Nine Months  Ended  September  30, 1996  Compared to the Nine Months  Ended
September 30, 1995

The comparisons for the nine months ended September 30, 1996 and the nine months
ended  September  30,  1995 are  consistent  with those  discussed  in the third
quarter 1996 compared to the third quarter 1995 except for the following:

Oil Revenue

Oil revenue increased  $117,000 during the first nine months of 1996 as compared
with the same period in 1995 due to a 26% increase in  production  due to higher
state  allowable  production  limits,  combined  with an increase in average oil
prices.  Average  oil prices  increased  from  $17.70 per barrel  during 1995 to
$20.53 per barrel during 1996.

Gas Revenue

Gas revenue increased  $345,000 during the first nine months of 1996 as compared
with the same period during 1995 due to a 33% increase in  production  resulting
from higher state  allowable  production  limits,  combined  with an increase in
average gas prices.  The average gas price  increased from $1.85 per mcf in 1995
to $3.09 per mcf in 1996.



                                                        -8-

<PAGE>




ITEM 1  -     LEGAL PROCEEDINGS

              Reference  is made to Item 8 - Note 3 of Form  10-K  for the  year
ended December 31, 1995.


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.



                                                        -9-

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


Date:   November 4, 1996                    By:        /s/Robert S. Pfeiffer
     ----------------------------------          -----------------------------
                                             Robert S. Pfeiffer, Vice President
                                                 (Principal Accounting Officer)



Document: P:\DOC\84-1MQ.DOC
                                                       -10-

<PAGE>