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

                                    Form 10-K

MARK ONE
     |X|         ANNUAL REPORT PURSUANT TO SECTION 13 or 15(d) OF THE
                 SECURITIES EXCHANGE ACT OF 1934 [FEE REQUIRED]

                   For the Fiscal Year Ended December 31, 1996

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

                         Commission File Number 0-89194


                         MAY DRILLING PARTNERSHIP 1984-2
                         MAY LIMITED PARTNERSHIP 1984-2
             (Exact name of registrant as specified in its charter)



                                                                      75-1985009
           Texas                                                      75-1985008
(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

           Securities Registered Pursuant to Section 12(b) of the Act:

                                                           Name of each exchange
Title of each class                                         on which registered
     None                                                                  None

           Securities Registered Pursuant to Section 12(g) of the Act:

                     Units of Participation, $1,000 Per Unit
                                (Title of Class)

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  |_|

Indicate by check mark if disclosure of delinquent  filers  pursuant to Item 405
of Regulation S-K is not contained herein and will not be contained, to the best
of  registrant's  knowledge,  in  definitive  proxy  or  information  statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. |X|


                                  Page 1 of 23


<PAGE>



                                       DOCUMENTS INCORPORATED BY REFERENCE:



                                                         Part of Form 10-K into
Document                                               which it is incorporated

The General Partnership Agreement and the Limited
Partnership Agreement filed as an Exhibit to
Registration Statement No. 0-89194                                      Part IV



                                                        -2-

<PAGE>



                                     PART I


ITEM 1 -      BUSINESS

May Drilling Partnership 1984-2 (the "Drilling or General  Partnership") and May
Limited  Partnership  1984-2 (the "Limited  Partnership")  were organized by May
Petroleum Inc. ("May") to explore for and develop oil and gas reserves primarily
in Texas, Oklahoma and Louisiana. Funds received from the sale and production of
oil and gas reserves are used to pay the obligations of the Limited Partnership.
Funds not required by the Limited Partnership as working capital are distributed
to the participants in the Drilling Partnership and the general partner.

The general  partner of the Limited  Partnership  is EDP  Operating,  Ltd.,
which is one of the operating  partnerships for Hallwood Energy Partners,  L. P.
("HEP").  The Drilling  Partnership  is the sole limited  partner of the Limited
Partnership. The Limited Partnership does not have any subsidiaries, nor does it
engage in any other kind of business.  The Limited  Partnership has no employees
and is operated by Hallwood  Petroleum,  Inc.  ("HPI"),  a subsidiary of HEP. In
February 1997, HPI employed 127 full-time employees.

Pursuant  to the terms of the  general  partnership  agreement  and the  limited
partnership  agreement,  HEP is  obligated,  from  time to time,  to  contribute
certain  amounts,  in property,  cash or unreimbursed  services,  to the Limited
Partnership.  As of December 31, 1996, all such required  contributions had been
accrued.

Participation in Expenses and Revenues

The principal expenses and revenues of the Limited Partnership are shared by the
general  partner  and the  Drilling  Partnership  as set forth in the  following
table.  The charges and credits to participants in the Drilling  Partnership are
shared  among the  participants  in  proportion  to their  ownership of units of
participation.
<TABLE>
<CAPTION>


                                                              Drilling               General
                                                            Partnership              Partner

<S>                                                             <C>                     <C>
Abandonment expenses (1)                                        99%                     1%
Noncapital expenses                                             99%                     1%
Direct expenses                                                 99%                     1%
Lease acquisition expenses                                                             100%
Capital expenses                                                                       100%
Oil and gas revenues                                            (2)                    (2)
Operating expenses                                              (2)                    (2)
Special projects                                                (2)                    (2)
General and administrative overhead                             (2)                    (2)
</TABLE>

     (1) Includes   expenses   that  would   otherwise  be  allocated  as  lease
         acquisition  expenses  and/or  capital  expenses  but  that  relate  to
         abandoned properties.

     (2) Such items were shared 70% by the Drilling  Partnership  and 30% by the
         general  partner until  December 31, 1984. As of December 31, 1984, and
         as of December 31 of each year thereafter, the sharing of such items is
         adjusted so the general partner's allocation equals the percentage that
         the amount of Limited  Partnership  expenses  allocated  to the general
         partner bears to the aggregate amount of Limited  Partnership  expenses
         allocated to the general partner and the Drilling Partnership,  plus 15
         percentage   points,  but  in  no  event  will  the  general  partner's
         allocation  exceed 50%.  The  sharing  ratio for each of the last three
         years was:


                                                        -3-

<PAGE>
<TABLE>
<CAPTION>




                                            1996               1995               1994
                                           ------             ------             -----

<S>                                        <C>                <C>                <C>  
Limited Partner                            68.4%              68.6%              68.8%
General Partner                            31.6%              31.4%              31.2%
</TABLE>

In 1997 the sharing ratio will be 68.2% to the limited  partner and 31.8% to the
general partner.

To  the  extent  that  the  characterization  of  any  expense  of  the  Limited
Partnership  depends on its deductibility  for federal income tax purposes,  the
proper  characterization  is determined by the general partner (according to its
intended  characterization  on the  Limited  Partnership's  federal  income  tax
return) in good faith at the time the expense is to be charged or credited. Such
characterization  will  control  related  charges  and  credits to the  partners
regardless of any subsequent  determination by the Internal Revenue Service or a
court of law that the reported  expenses should be otherwise  characterized  for
tax purposes.

Competition

Oil and gas must  compete with coal,  atomic  energy,  hydro-electric  power and
other  forms of energy.  See also  "Marketing"  for a  discussion  of the market
structure for oil and gas sales.

Regulation

Production and sale of oil and gas is subject to federal and state  governmental
regulations in a variety of ways including environmental regulations, labor law,
interstate  sales,  excise taxes and federal and Indian lands royalty  payments.
Failure to comply with these  regulations  may result in fines,  cancellation of
licenses to do business and cancellation of federal, state or Indian leases.

The  production of oil and gas is subject to regulation by the state  regulatory
agencies in the states in which the Limited  Partnership  does  business.  These
agencies  make and enforce  regulations  to prevent  waste of oil and gas and to
protect the rights of owners to produce oil and gas from a common reservoir. The
regulatory  agencies  regulate  the amount of oil and gas  produced by assigning
allowable production rates to wells capable of producing oil and gas.

Federal Income Tax Considerations

The Limited Partnership and the General Partnership are partnerships for federal
income tax purposes.  Consequently,  they are not taxable entities;  rather, all
income, gains, losses,  deductions and credits are passed through and taken into
account by the  partners on their  individual  federal  income tax  returns.  In
general,  distributions are not subject to tax so long as such  distributions do
not exceed the partner's  adjusted tax basis. Any distributions in excess of the
partner's adjusted tax basis are taxed generally as capital gains.

Marketing

The oil and gas produced from the  properties  owned by the Limited  Partnership
has typically been marketed  through normal channels for such products.  Oil has
generally  been sold to  purchasers  at field  prices  posted  by the  principal
purchasers of crude oil in the areas where the producing properties are located.
The majority of the Limited  Partnership's  gas  production  is sold on the spot
market and is transported in intrastate and interstate  pipelines.  Both oil and
natural gas are purchased by refineries,  major oil companies,  public utilities
and other users and processors of petroleum products.



                                                        -4-

<PAGE>



Factors  which,  if they were to  occur,  might  adversely  affect  the  Limited
Partnership  include  decreases  in oil and gas prices,  the  availability  of a
market  for  production,  rising  operational  costs of  producing  oil and gas,
compliance with and changes in environmental  control  statutes,  and increasing
costs and difficulties of transportation.

Significant Customers

For the years ended  December 31, 1996,  1995 and 1994  purchases by each of the
following  companies  exceeded  10% of the  total  oil and gas  revenues  of the
Limited Partnership.
<TABLE>
<CAPTION>


                                            1996               1995               1994
                                           ------             ------             -----

<S>                                         <C>                <C>                <C>
Conoco Inc.                                 56%                72%                60%
TXG Gas Marketing                           30%
Koch Oil Company                                                                  20%
</TABLE>

Although the Limited Partnership sells the majority of its production to a small
number of purchasers,  there are numerous  other  purchasers in the area, so the
loss  of any  significant  customer  would  not  adversely  affect  the  Limited
Partnership's operations.

Environmental Considerations

The  exploration  for, and  development  of, oil and gas involve the extraction,
production and transportation of materials which, under certain conditions,  can
be  hazardous or can cause  environmental  pollution  problems.  In light of the
present general interest in environmental  problems,  the general partner cannot
predict what effect  possible  future  public or private  action may have on the
business of the Limited  Partnership.  The general partner is continually taking
actions it  believes  necessary  in its  operations  to ensure  conformity  with
applicable  federal,  state and  local  environmental  regulations  and does not
presently  anticipate  that  the  compliance  with  federal,   state  and  local
environmental  regulations  will have a material  adverse  effect  upon  capital
expenditures, earnings or the competitive position of the Limited Partnership in
the oil and gas industry.

Insurance Coverage

The Limited  Partnership is subject to all the risks inherent in the exploration
for,  and  development  of,  oil and gas,  including  blowouts,  fires and other
casualties. The Limited Partnership maintains insurance coverage as is customary
for  entities of a similar  size  engaged in  operations  similar to the Limited
Partnership's,  but  losses can occur  from  uninsurable  risks or in amounts in
excess of existing insurance  coverage.  The occurrence of an event which is not
insured  or not fully  insured  could have an adverse  impact  upon the  Limited
Partnership's earnings and financial position.


ITEM 2  -     PROPERTIES

The Limited  Partnership's oil and gas reserves are concentrated in one prospect
in south  Louisiana.  Natural gas  accounts  for 67% of  estimated  future gross
revenues in the Limited Partnership's reserve report as of December 31, 1996.


                                                        -5-

<PAGE>



Significant Prospect

At December 31, 1996,  the following  prospect  accounted for all of the Limited
Partnership's proved oil and gas reserves. Reserve quantities were obtained from
the December 31, 1996 reserve report prepared by HPI's petroleum engineers.

Montet Prospect. The Montet prospect is located in Lafayette Parish,  Louisiana.
The Limited Partnership's  interest in the prospect contains one productive well
(the Freddie  Aker) and has estimated  remaining  net proved  reserves of 33,000
bbls  of oil  and  345,000  mcf of gas as of  December  31,  1996.  The  Limited
Partnership's working interest in this well is 13.1%. The prospect produces from
one zone, the Bol Mex 3 formation at 15,275 feet.


ITEM 3  -     LEGAL PROCEEDINGS

For a description of legal proceedings affecting The Limited Partnership, please
refer to Item 8--Note 4.


ITEM 4  -     SUBMISSION OF MATTERS TO A VOTE OF STOCKHOLDERS

No matter was submitted to a vote of  participants  during the fourth quarter of
1996.


                                                      PART II


ITEM 5 -      MARKET FOR THE REGISTRANT'S COMMON EQUITY AND RELATED STOCKHOLDER
              MATTERS

     a)  The registrant's  securities consist of partnership interests which are
         not traded on any exchange and for which no established  public trading
         market exists.

     b)  As of December 31, 1996, there were approximately 731 holders of record
         of partnership interests in the Drilling Partnership.

     c)  Distributions  paid by the  Limited  Partnership  were as  follows  (in
           thousands):


                              General            Limited
                              Partner            Partner

       1996                      $524             $1,078
       1995                       336                676
       1994                       428                894



                                                        -6-

<PAGE>



ITEM 6 - SELECTED FINANCIAL DATA
<TABLE>
<CAPTION>


                                                                For the Limited Partnership
                                                          As of or for the Year Ended December 31,
                                                         -----------------------------------------
                                        1996              1995              1994              1993              1992
                                       ------            ------            ------            ------            -----
                                                                       (In thousands)

<S>                                          <C>              <C>               <C>               <C>               <C>   
Total revenues                               $2,010           $1,170            $1,446            $1,110            $1,696
Oil and gas revenues                          1,996            1,156             1,437             1,101             1,688
Net income                                    1,796              988             1,270               921             1,363
Working capital                                 806              580               577               603             1,035
Total assets                                    818              597               591               618             1,082
Partners' capital                               806              580               577               603             1,066

</TABLE>

ITEM 7 -      MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
              RESULTS OF OPERATIONS

Liquidity and Capital Resources

Material changes in the Limited  Partnership's cash position for the years ended
December 31, 1996 and 1995 are summarized as follows:
<TABLE>
<CAPTION>


                                                             1996               1995
                                                            ------             -----
                                                                  (In thousands)

<S>                                                              <C>               <C>     
Cash provided by operating activities                            $ 1,687           $    962
Distributions to partners                                        (1,602)            (1,012)
Contributions from partners                                           27                 26
Additions to oil and gas properties                                 (10)                (2)
                                                                -------            -------
Increase (decrease) in cash                                      $   102           $   (26)
                                                                  ======            ======
</TABLE>

Cash  provided  by  operating   activities  in  1996  was  used   primarily  for
distributions  to the  partners.  Future  distributions  depend on,  among other
things,  continuation  of current or higher oil and gas prices and  markets  for
production.

The  Limited  Partnership  has net working  capital of $806,000 at December  31,
1996. This working capital,  together with cash flows generated from operations,
may be used to fund future distributions.

Proved  reserves and discounted  future net revenues  valued at year-end  prices
(discounted at 10% and before general and administrative  expenses) attributable
to proved  reserves  were  estimated  at 33,000  bbls and  345,000 mcf valued at
$2,146,000 in 1996 and 34,000 bbls and 335,000 mcf valued at $1,243,000 in 1995.
The  Partnership's  oil and gas reserves  were revised  upward during 1996 based
upon the continued performance of the Freddie Aker well.



                                                        -7-

<PAGE>



Results of Operations

1996 Compared to 1995

Oil Revenue

Oil revenue  increased  $211,000 during 1996 as compared with 1995. The increase
is comprised of a 15% increase in  production,  combined with an increase in the
average  price from $17.67 per barrel in 1995 to $21.40 per barrel in 1996.  The
increase in production  from 30,712 barrels in 1995 to 35,244 barrels in 1996 is
primarily due to increased state allowable production limits partially offset by
normal production declines.

Gas Revenue

Gas revenue  increased  $629,000 during 1996 as compared with 1995. The increase
is due to an increase in the average gas price from $1.98 per mcf during 1995 to
$3.15 per mcf during  1996  combined  with a 28%  increase  in  production.  The
increase in production from 309,054 mcf in 1995 to 394,446 mcf in 1996 is due to
increased  state  allowable   production   limits  partially  offset  by  normal
production declines.

Lease Operating

Lease  operating  expense  increased  $8,000  during 1996 as compared  with 1995
primarily due to increased maintenance activity during 1996.

Production Taxes

Production taxes increased $33,000 during 1996 as compared with 1995 as a result
of increased oil and gas production during 1996.

General and Administrative

General and  administrative  expenses  decreased $10,000 during 1996 as compared
with 1995  primarily  due to a decrease in the  allocation  of overhead from the
general partner.

Depletion

Depletion  expense  increased $8,000 during 1996 as compared with 1995 due to an
increase in capitalized costs during 1996.

1995 Compared to 1994

Oil Revenue

Oil revenue decreased $32,000 during 1995 as compared with 1994. The decrease is
comprised of a 14% decrease in  production,  partially  offset by an increase in
the  average  price from $16.18 per barrel in 1994 to $17.67 per barrel in 1995.
The decrease in production from 35,520 barrels in 1994 to 30,712 barrels in 1995
is primarily due to decreased  state allowable  production  limits combined with
normal production declines.



                                                        -8-

<PAGE>



Gas Revenue

Gas revenue  decreased  $249,000 during 1995 as compared with 1994. The decrease
is due to a decrease  in the average gas price from $2.27 per mcf during 1994 to
$1.98 per mcf during  1995  combined  with a 19%  decrease  in  production.  The
decrease in production from 380,349 mcf in 1994 to 309,054 mcf in 1995 is due to
decreased  state  allowable  production  limits  as  well as  normal  production
declines.

Lease Operating

Lease  operating  expense  increased  $3,000  during 1995 as compared  with 1994
primarily due to increased maintenance activity during 1995.

Production Taxes

Production  taxes decreased $6,000 during 1995 as compared with 1994 as a result
of decreased oil and gas revenue during 1995.

General and Administrative

General and  administrative  expenses  increased  $2,000 during 1995 as compared
with 1994  primarily  due to an increase in the  allocation of overhead from the
general partner.

Depletion

Depletion  expense  increased $2,000 during 1995 as compared with 1994 due to an
increase in capitalized costs during 1995.

Litigation Settlement

Litigation  settlement  expense  during 1995  represents  the costs of a lawsuit
settlement which is further discussed in Item 8 - Note 4 of this Form 10-K.



                                                        -9-

<PAGE>



ITEM 8 - FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA
<TABLE>
<CAPTION>

                                           INDEX TO FINANCIAL STATEMENTS

                                                                                                               Page
                                               FINANCIAL STATEMENTS:


<S>                                                                                                              <C>
     Independent Auditors' Report                                                                                11

     Balance Sheets at December 31, 1996 and 1995 -
         May Drilling Partnership 1984-2                                                                         12

     Balance Sheets at December 31, 1996 and 1995 -
         May Limited Partnership 1984-2                                                                          13

     Statements of Operations for the Years Ended
         December 31, 1996, 1995 and 1994 -
         May Limited Partnership 1984-2                                                                          14

     Statements of Changes in Partners' Capital for the Years Ended December 31,
         1996, 1995 and 1994 -
         May Limited Partnership 1984-2                                                                          15

     Statements of Cash Flows for the Years Ended
         December 31, 1996, 1995 and 1994 -
         May Limited Partnership 1984-2                                                                          16

     Notes to Financial Statements - May Drilling Partnership 1984-2
         and May Limited Partnership 1984-2                                                                   17-20

SUPPLEMENTAL OIL AND GAS RESERVE INFORMATION (UNAUDITED)                                                         21

</TABLE>

                                                       -10-

<PAGE>



                                           INDEPENDENT AUDITORS' REPORT



To the Partners of May Drilling Partnership 1984-2 and
     May Limited Partnership 1984-2:

We have audited the  financial  statements  of May Drilling  Partnership  1984-2
("General   Partnership")   and  May  Limited   Partnership   1984-2   ("Limited
Partnership")  as of December  31, 1996 and 1995 and for each of the three years
in the period ended December 31, 1996, listed in the accompanying  index at Item
8.  These  financial  statements  are the  responsibility  of the  Partnerships'
management.  Our  responsibility  is to express  an  opinion on these  financial
statements based on our audits.

We  conducted  our  audits  in  accordance  with  generally   accepted  auditing
standards.  Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement.  An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements.  An audit also includes
assessing the  accounting  principles  used and  significant  estimates  made by
management,  as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.

In our  opinion,  such  financial  statements  present  fairly,  in all material
respects,  the  financial  position of the General  Partnership  and the Limited
Partnership  at December 31, 1996 and 1995,  and the results of  operations  and
cash flows of the Limited  Partnership for each of the three years in the period
ended  December  31,  1996 in  conformity  with  generally  accepted  accounting
principles.



DELOITTE & TOUCHE LLP

Denver, Colorado
February 28, 1997


                                                       -11-

<PAGE>
<TABLE>
<CAPTION>



                                          MAY DRILLING PARTNERSHIP 1984-2
                                                  BALANCE SHEETS
                                                  (In thousands)



                                                                      December 31,                December 31,
                                                                          1996                         1995

ASSETS
<S>                                                                       <C>                         <C> 
Investment in May Limited Partnership 1984-2                              $445                        $296
                                                                           ===                         ===


PARTNERS' CAPITAL
Partners' Capital                                                         $445                        $296
                                                                           ===                         ===






<FN>

Note:    The  statements of  operations,  changes in partners'  capital and cash
         flows for May Drilling  Partnership  1984-2 are not  presented  because
         such  information  is  equal  to the  Limited  Partners'  share of such
         activity as presented in the May Limited  Partnership  1984-2 financial
         statements.  The May Drilling Partnership carries its investment in May
         Limited  Partnership  1984-2  on the  equity  method.  The May  Limited
         Partnership  1984-2 financial  statements should be read in conjunction
         with this balance sheet.
</FN>






















<FN>

                                   The     accompanying  notes  are an  integral
                                           part of the financial statements.
</FN>
</TABLE>

                                                       -12-

<PAGE>

<TABLE>
<CAPTION>


                                          MAY LIMITED PARTNERSHIP 1984-2
                                                  BALANCE SHEETS
                                                  (In thousands)



                                                                      December 31,                December 31,
                                                                          1996                         1995

ASSETS
CURRENT ASSETS
<S>                                                                               <C>                          <C>    
     Cash and cash equivalents                                                    $    352                     $   250
     Accrued oil and gas revenues                                                      320                         245
     Due from affiliate                                                                114                          75
     Contributions receivable from general partner                                      32                          27
                                                                                  --------                      ------
              Total                                                                    818                         597
                                                                                   -------                      ------

OIL AND GAS PROPERTIES, using the
     full cost method of accounting                                                 10,369                      10,359
         Less accumulated depletion                                               (10,369)                    (10,359)
                                                                                  -------                     -------
              Net oil and gas properties

TOTAL ASSETS                                                                     $     818                    $    597
                                                                                  ========                     =======

LIABILITIES AND PARTNERS' CAPITAL
CURRENT LIABILITIES
     Accounts payable and accrued liabilities                                    $      12                    $     17
                                                                                  --------                     -------

PARTNERS' CAPITAL
     General Partner                                                                   361                         284
     Limited Partner                                                                   445                         296
                                                                                   -------                     -------
              Total                                                                    806                         580
                                                                                   -------                     -------

TOTAL LIABILITIES AND PARTNERS' CAPITAL                                           $    818                    $    597
                                                                                   =======                     =======















<FN>

                                   The     accompanying  notes  are an  integral
                                           part of the financial statements.
</FN>
</TABLE>

                                                       -13-

<PAGE>

<TABLE>
<CAPTION>


                                          MAY LIMITED PARTNERSHIP 1984-2
                                             STATEMENTS OF OPERATIONS
                               FOR THE YEARS ENDED DECEMBER 31, 1996, 1995 AND 1994
                                         (In thousands, except for Units)



                                                             1996                   1995                  1994
                                                            ------                 ------                -----

REVENUES
<S>                                                               <C>                    <C>                   <C>     
     Oil revenue                                                  $    754               $    543              $    575
     Gas revenue                                                     1,242                    613                   862
     Interest income                                                    14                     14                     9
                                                                  --------               --------              --------
              Total                                                  2,010                  1,170                 1,446
                                                                    ------                 ------                ------

COSTS AND EXPENSES
     Lease operating                                                    33                     25                    22
     Production taxes                                                  125                     92                    98
     General and administrative                                         36                     46                    44
     Depletion                                                          10                      2
     Litigation settlement                                                                      7
     Professional services and other                                    10                     10                    12
                                                                  --------               --------              --------
              Total                                                    214                    182                   176
                                                                   -------                -------               -------

NET INCOME                                                         $ 1,796               $    988               $ 1,270
                                                                    ======                =======                ======

ALLOCATION OF NET INCOME:
     General Partner                                              $    569                $   313              $    398
                                                                   =======                 ======               =======
     Limited Partner                                               $ 1,227                $   675              $    872
                                                                    ======                 ======               =======
     Per initial $1,000 Limited Partner
         investment                                                $142.13                $ 78.19               $101.01
                                                                    ======                 ======                ======
     Weighted average initial $1,000 Limited
         Partner investment units outstanding                        8,633                  8,633                 8,633
                                                                    ======                 ======               =======

















<FN>
                                   The     accompanying  notes  are an  integral
                                           part of the financial statements.
</FN>
</TABLE>

                                                       -14-

<PAGE>


<TABLE>
<CAPTION>

                                          MAY LIMITED PARTNERSHIP 1984-2
                                    STATEMENTS OF CHANGES IN PARTNERS' CAPITAL
                               FOR THE YEARS ENDED DECEMBER 31, 1996, 1995 AND 1994
                                                  (In thousands)



                                                            General                Limited
                                                            Partner                Partner                Total

<S>                                                                  <C>                 <C>                   <C>     
BALANCE, December 31, 1993                                           $ 284               $    319              $    603
     Capital contributions                                              26                                           26
     Net income                                                        398                    872                 1,270
     Distributions                                                   (428)                  (894)               (1,322)
                                                                    -----                -------                ------

BALANCE, December 31, 1994                                             280                    297                   577
     Capital contributions                                              27                                           27
     Net income                                                        313                    675                   988
     Distributions                                                   (336)                  (676)               (1,012)
                                                                    -----                -------                ------

BALANCE, December 31, 1995                                             284                    296                   580
     Capital contributions                                              32                                           32
     Net income                                                        569                  1,227                 1,796
     Distributions                                                   (524)                (1,078)               (1,602)
                                                                    -----                 ------                ------

BALANCE, December 31, 1996                                          $  361               $    445              $   806
                                                                     =====                =======               ======























<FN>

                                   The     accompanying  notes  are an  integral
                                           part of the financial statements.
</FN>
</TABLE>

                                                       -15-

<PAGE>


<TABLE>
<CAPTION>

                                          MAY LIMITED PARTNERSHIP 1984-2
                                             STATEMENTS OF CASH FLOWS
                               FOR THE YEARS ENDED DECEMBER 31, 1996, 1995 AND 1994
                                                  (In thousands)



                                                                    1996                   1995                  1994
                                                                   ------                 ------                -----

OPERATING ACTIVITIES:
<S>                                                                <C>                   <C>                    <C>    
     Net income                                                    $ 1,796               $    988               $ 1,270
     Adjustment to reconcile net income
         to net cash provided by operating
         activities:
              Depletion                                                 10                      2
                                                                  --------               --------
                  Cash from operations before
                      working capital changes                        1,806                    990                 1,270

     Changes in assets and liabilities provided (used) cash:
         Accrued oil and gas revenues                                 (75)                   (42)                   101
         Due from affiliate                                           (39)                     11                  (35)
         Accounts payable and accrued
              liabilities                                              (5)                      3                   (1)
                                                                 --------                --------             --------
                  Net cash provided by
                      operating activities                           1,687                    962                 1,335
                                                                    ------                -------                ------

INVESTING ACTIVITIES:
     Additions to oil and gas properties                              (10)                    (2)
                                                                 --------               --------

FINANCING ACTIVITIES:
     Distributions to partners                                     (1,602)                (1,012)               (1,322)
     Contributions from partners                                        27                     26                    23
                                                                  --------               --------              --------
                  Net cash used in financing
                      activities                                   (1,575)                  (986)               (1,299)
                                                                   ------                -------                ------

NET INCREASE (DECREASE) IN CASH
     AND CASH EQUIVALENTS                                              102                   (26)                    36

CASH AND CASH EQUIVALENTS:

     BEGINNING OF YEAR                                                 250                    276                   240
                                                                   -------                -------               -------

     END OF YEAR                                                  $    352               $    250              $    276
                                                                   =======                =======               =======






<FN>

                                   The     accompanying  notes  are an  integral
                                           part of the financial statements.
</FN>
</TABLE>

                                                       -16-

<PAGE>



                                         MAY DRILLING PARTNERSHIP 1984-2
                                                        AND
                                          MAY LIMITED PARTNERSHIP 1984-2

                                           NOTES TO FINANCIAL STATEMENTS


(1)  ACCOUNTING POLICIES AND OTHER MATTERS

         General Partnership

         May Drilling  Partnership  1984-2,  a Texas  general  partnership  (the
         "General Partnership"), was organized by May Petroleum Inc. ("May") for
         the purpose of oil and gas exploration  through May Limited Partnership
         1984-2 (the "Limited Partnership").  The General Partnership was formed
         on September 18, 1984, with investors  ("Participants")  subscribing an
         aggregate  of  $8,633,000  in  assessable   $1,000  units.   After  the
         expenditure  of  the  initial   contributions   of  the   Participants,
         additional mandatory assessments from each Participant are provided for
         under the terms of the general partnership agreement in an amount up to
         25% of the initial  contribution of the  Participant.  During 1985, May
         assessed the  Participants 5% of initial  contributions.  No additional
         assessments have been made since 1985.

         The general partnership  agreement requires that the manager,  Hallwood
         Energy  Partners,  L.  P.  ("HEP"),  offer  to  repurchase  partnership
         interests  from  Participants  for cash at amounts to be  determined by
         appraisal  (as set forth in the  partnership  agreement) of the Limited
         Partnership's  net assets no later than  December 31, 1988,  and during
         each succeeding year, if such net assets are positive.  The manager has
         made  repurchase  offers in each year since 1989 and  intends to make a
         repurchase offer in 1997.

         As the General  Partnership is the sole limited  partner of the Limited
         Partnership,  its results of operations,  changes in partners'  capital
         and cash flows are equal to the limited  partner's share of the Limited
         Partnership's  results of operations,  changes in partners' capital and
         cash  flows as set forth  herein.  Therefore,  separate  statements  of
         operations,  changes  in  partners'  capital  and  cash  flows  are not
         presented for the General Partnership.

         Limited Partnership

         The Limited Partnership, a Texas limited partnership,  was organized by
         May  and  the  General  Partnership,  for  the  purpose  of oil and gas
         exploration and the production of crude oil,  natural gas and petroleum
         products.   The  Limited   Partnership's   oil  and  gas  reserves  are
         concentrated  in one prospect in south  Louisiana.  Among other things,
         the terms of the Limited  Partnership  agreement (the "Agreement") give
         the general  partner the authority to borrow funds.  The Agreement also
         requires that the general partner's total capital  contributions to the
         Limited Partnership as of each year end, including  unrecovered general
         partner  acreage  and  equipment  advances,  must be  compared to total
         Limited  Partnership  expenditures  from inception to date, and if such
         contributions  are less than 15% of such  expenditures,  an  additional
         contribution  in  the  amount  of the  deficiency  is  required.  As of
         December 31, 1996, all such contributions had been accrued.

         On June 30, 1987,  May sold to HEP all of its economic  interest in the
         Limited  Partnership  and  account  receivable  balances  due  from the
         Limited  Partnership.  HEP became the  general  partner of the  Limited
         Partnership in 1988.



                                                       -17-

<PAGE>



         Sharing of Costs and Revenues

         Capital costs, as defined by the Agreement, for commercially productive
         wells  and  the  costs  related  to the  organization  of  the  Limited
         Partnership  are borne by the  general  partner.  Noncapital  costs and
         direct  expenses,  as defined by the  Agreement,  are charged 1% to the
         general  partner  and 99% to the  limited  partner.  Oil and gas sales,
         operating expenses and general and  administrative  overhead are shared
         so that the general partner's allocation will equal the percentage that
         the amount of Limited Partnership  expenses,  as defined,  allocated to
         the  general   partner  bears  to  the  aggregate   amount  of  Limited
         Partnership  expenses  allocated to the general partner and the limited
         partner,  plus 15 percentage  points,  but in no event will the general
         partner's allocation exceed 50%. The sharing ratio for each of the last
         three years was as follows:
<TABLE>
<CAPTION>


                                            1996               1995               1994
                                           ------             ------             -----

<S>                                        <C>                <C>                <C>  
Limited Partner                            68.4%              68.6%              68.8%
General Partner                            31.6%              31.4%              31.2%
</TABLE>

         Significant Customers

         For the years ended December 31, 1996, 1995 and 1994, purchases by each
         of the  following  companies  exceeded  10% of the  total  oil  and gas
         revenues of the Limited Partnership:

<TABLE>
<CAPTION>

                                            1996               1995               1994
                                           ------             ------             -----

<S>                                         <C>                <C>                <C>
Conoco Inc.                                 56%                72%                60%
TXG Gas Marketing                           30%
Koch Oil Company                                                                  20%
</TABLE>

         Although the Limited  Partnership  sells the majority of its production
         to a small number of purchasers, there are numerous other purchasers in
         the area, so the loss of any  significant  customer would not adversely
         affect the Limited Partnership's operations.

         Income Taxes

         No  provision  for federal  income  taxes is included in the  financial
         statements  of  the  Limited  Partnership  or the  General  Partnership
         because,  as  partnerships,  they are not subject to federal income tax
         and the tax effects of their  activities  accrue to the  partners.  The
         partnerships' tax returns, the qualification of the General and Limited
         Partnerships as partnerships  for federal income tax purposes,  and the
         amount of taxable  income or loss are subject to examination by federal
         and state taxing authorities. If such examinations result in changes to
         the  partnerships'  taxable  income or loss,  the tax  liability of the
         partners could change accordingly.

         Oil and Gas Properties

         The Limited  Partnership follows the full cost method of accounting for
         oil  and  gas  properties  and,  accordingly,   capitalizes  all  costs
         associated  with  the  exploration  and  development  of  oil  and  gas
         reserves.

         The capitalized costs of evaluated properties,  including the estimated
         future costs to develop proved reserves,  are amortized on the units of
         production  basis.  Full cost  amortization per dollar of gross oil and
         gas revenues was $.01 in 1996 and 1995, and $-0- in 1994.



                                                       -18-

<PAGE>



         Capitalized  costs are  limited to an amount not to exceed the  present
         value of estimated  future net cash flows. No valuation  adjustment was
         required in 1996, 1995 or 1994.

         Generally no gains or losses are  recognized on the sale or disposition
         of oil and gas properties.  Maintenance and repairs are charged against
         income when incurred.

         Gas Balancing

         The Limited  Partnership  uses the sales method for  accounting for gas
         balancing.  Under  this  method,  the  Limited  Partnership  recognizes
         revenue on all of its sales of production,  and any over  production or
         under production is recovered at a future date.

         As of December 31, 1996, the net imbalance to the Limited Partnership's
         interest is not considered material.  Current imbalances can be made up
         with production from the existing well.

         Use of Estimates

         The preparation of the financial statements for the Limited Partnership
         and  General   Partnership  in  conformity   with  generally   accepted
         accounting   principles  requires  management  to  make  estimates  and
         assumptions  that affect the reported amounts of assets and liabilities
         and disclosure of contingent  assets and liabilities at the date of the
         financial  statements and the reported amounts of revenues and expenses
         during the  reporting  period.  Actual  results could differ from these
         estimates.

         Related Party Transactions

         Hallwood Petroleum,  Inc. ("HPI"), a subsidiary of the general partner,
         pays all costs and  expenses of  operations  and  receives all revenues
         associated with the Limited Partnership's properties. At month end, HPI
         distributes revenues in excess of costs to the Limited Partnership. The
         amounts due from HPI were  $114,000 and $75,000 as of December 31, 1996
         and 1995,  respectively.  These  balances  represent  net revenues less
         operating costs and expenses.

         Cash Flows

         All highly liquid  investments  purchased with an original  maturity of
         three months or less are considered to be cash equivalents.

         Reclassifications

         Certain  reclassifications  have been made to prior  years'  amounts to
         conform to the classifications used in the current year.


(2)  GENERAL AND ADMINISTRATIVE OVERHEAD

         HPI conducts the day to day operations of the Limited  Partnership  and
         other  affiliated  partnerships  of HEP.  The  costs of  operating  the
         entities are allocated to each entity based upon the time spent on that
         entity.  General and  administrative  overhead  allocated by HPI to the
         Limited  Partnership  totaled  $36,000  in  1996,  $46,000  in 1995 and
         $44,000 in 1994.



                                                       -19-

<PAGE>




(3)  INCOME TAXES

         As a result of the  differences in the accounting  treatment of certain
         items for  income  tax  purposes  as  opposed  to  financial  reporting
         purposes, primarily depreciation, depletion and amortization of oil and
         gas properties and the  recognition of intangible  drilling costs as an
         expense or capital item, the income tax basis of oil and gas properties
         differs  from the  basis  used for  financial  reporting  purposes.  At
         December 31, 1996 and 1995,  the income tax bases of the  Partnership's
         oil  and  gas  properties   were   approximately   $6,800  and  $4,900,
         respectively.


(4)  LITIGATION SETTLEMENT

         In the fourth quarter of 1995,  the parties  settled the lawsuit styled
         Stutes v. Hallwood Petroleum,  Inc. et al. The plaintiff in the lawsuit
         alleged that as a result of exposure to benzene in the petroleum he was
         hauling  from   various   wells  owned  and  operated  by  the  Limited
         Partnership  and  the  approximately  80  other  named  defendants,  he
         contracted myelogenous leukemia. The Limited Partnership's share of the
         settlement not covered by insurance was $7,000.

                                                       -20-

<PAGE>



                                   SUPPLEMENTAL OIL AND GAS RESERVE INFORMATION
                                                    (Unaudited)


The following  tables contain certain costs and reserve  information  related to
the Limited Partnership's oil and gas activities. The Limited Partnership has no
long-term  supply  agreements  and all  reserves  are located  within the United
States.

Costs Incurred -

<TABLE>
<CAPTION>

                                                                      For the Years Ended December 31,
                                                             1996                   1995                  1994
                                                            ------                 ------                -----
                                                                               (In thousands)

<S>                                                           <C>                    <C>                   <C>
Development costs                                             $10                    $ 2                   $
                                                               ==                     ==
</TABLE>

Oil and Gas Reserves (valued at year-end prices discounted at 10%) -

<TABLE>
<CAPTION>

                                                           1996                            1995                            1994
                                                          ------                          ------                          -----
                                           Bbls            Mcf             Bbls            Mcf             Bbls            Mcf

Total Proved Reserves:
<S>                                           <C>            <C>              <C>            <C>              <C>            <C>
     Beginning of period                      34             335              31             280              26             227
     Revisions to previous estimates          34             404              34             364              41             433
     Production                              (35)           (394)            (31)           (309)            (36)           (380)
                                             ---            ----             ---            ----             ---            ----
         End of Period                        33             345              34             335              31             280
                                             ===            ====             ===            ====             ===            ====

Proved Developed Reserves:
         Beginning of period                  34             335              31             280              26             227
                                             ===            ====             ===            ====             ===            ====
         End of period                        33             345              34             335              31             280
                                             ===            ====             ===            ====             ===            ====
</TABLE>

Certain reserve value  information is provided  directly to partners pursuant to
the Agreement. Accordingly, such information is not presented herein.


                                                       -21-

<PAGE>



ITEM 9 -      DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND FINANCIAL
              DISCLOSURE

              None.


                                                     PART III


ITEM 10 -     DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT

              The Drilling  Partnership  and Limited  Partnership are managed by
              affiliates of HEP and do not have directors or executive officers.


ITEM 11 -     EXECUTIVE COMPENSATION

              The partnerships  pay no salaries or other direct  remuneration to
              officers,  directors or key  employees  of the general  partner or
              HPI. The Limited  Partnership  reimburses the general  partner for
              general  and  administrative  costs  incurred  on  behalf  of  the
              partnerships. See Note 2 to the Financial Statements.


ITEM 12 -     SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

              To the knowledge of the general partner,  no person owns of record
              or  beneficially  more  than  5%  of  the  Drilling  Partnership's
              outstanding units, other than HEP, the address of which is 4582 S.
              Ulster  Street  Parkway,   Denver,   Colorado  80237,   and  which
              beneficially owns  approximately  33.3% of the outstanding  units.
              The general partner of HEP is HEPGP Ltd.


ITEM 13 -     CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

              For  information  with respect to the Limited  Partnership and its
              relationships and transactions with the general partner,  see Part
              I, Item 1 and Part II, Item 7.


                                                      PART IV


ITEM 14 -     EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K

         a.   Financial Statements and Schedules:
              See Index at Item 8.

         b.   Reports on Form 8-K - None.

         c.   Exhibits:

               3.1 The General Partnership Agreement and the Limited Partnership
                   Agreement filed as an Exhibit to  Registration  Statement No.
                   0-89194,  are  incorporated herein by reference.


                                                       -22-

<PAGE>


SIGNATURES

Pursuant to the  requirements of Section 13 or 15(d) of the Securities  Exchange
Act of 1934,  as amended,  the  Partnerships  have duly caused this report to be
signed on their behalf by the undersigned, thereunto duly authorized.


                         MAY DRILLING PARTNERSHIP 1984-2
                         MAY LIMITED PARTNERSHIP 1984-2
                               By:      EDP OPERATING, LTD., GENERAL PARTNER
                               By:      HALLWOOD G.P., Inc.
                                        General Partner



                           By: /s/William L. Guzzetti
                               William L. Guzzetti
                                President, Chief Executive Officer and Director


Pursuant to the requirements of the Securities Exchange Act of 1934, this report
has been signed below by the following  persons on behalf of the  registrant and
in the capacities and on the dates indicated.


Signature                           Title                           Date



/s/Robert S. Pfeiffer           Vice President                February 28, 1997
----------------------                                        -----------------
Robert S. Pfeiffer         (Principal Accounting Officer)


Document:P:\\DOC\MAY84-2K.DOC
                                                       -23-

<PAGE>