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 2-89194


                         MAY DRILLING PARTNERSHIP 1984-3
                         MAY LIMITED PARTNERSHIP 1984-3
             (Exact name of registrant as specified in its charter)



                                                                      75-1994687
             Texas                                                    75-1994682
(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. 2-89194                                       Part IV


                                       -2-

<PAGE>



                                     PART I


ITEM 1 - BUSINESS

May Drilling Partnership 1984-3 (the "Drilling or General  Partnership") and May
Limited  Partnership  1984-3 (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 shown 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                            66.4%              66.7%              66.9%
General Partner                            33.6%              33.3%              33.1%
</TABLE>

In 1997, the sharing ratio will be 66.1% to the limited partner and 33.9% 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,  state 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.

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.


                                                        -5-

<PAGE>



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 37,000
bbls  of oil  and  395,000  mcf of gas as of  December  31,  1996.  The  Limited
Partnership's  working interest in this well is 15%. 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  531 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                      $638             $1,202
       1995                       407                758
       1994                       523                991


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                               $2,301           $1,338            $1,657            $1,271            $1,941
Oil and gas revenues                          2,286            1,323             1,646             1,261             1,932
Net income                                    2,063            1,139             1,462             1,065             1,577
Working capital                                 913              654               650               673             1,224
Total assets                                    925              670               664               688             1,272
Partners' capital                               913              654               650               673             1,257

</TABLE>


                                                        -6-

<PAGE>



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                            $ 1,939            $ 1,108
Distributions to partners                                        (1,840)            (1,165)
Contributions from partners                                           30                 29
Additions to oil and gas properties                                 (12)                (3)
                                                               --------           --------
Increase (decrease) in cash                                     $    117          $    (31)
                                                                 -------           =======
</TABLE>

Cash  provided  by  operating   activities  in  1996  was  used   primarily  for
distributions to 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 $913,000 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 37,000  bbls and  395,000 mcf valued at
$2,457,000 in 1996 and 39,000 bbls and 383,000 mcf valued at $1,423,000 in 1995.
The  Partnership's  oil and gas reserves  were revised  upward during 1996 based
upon the continued performance of the Freddie Aker well.

Results of Operations

1996 Compared to 1995

Oil Revenue

Oil revenue  increased  $243,000 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 35,169 barrels in 1995 to 40,359 barrels in 1996 is
primarily due to increased state allowable production limits partially offset by
normal production declines.

Gas Revenue

Gas revenue  increased  $720,000 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 353,904 mcf in 1995 to 451,691 mcf in 1996 is due to
increased  state  allowable   production   limits  partially  offset  by  normal
production declines.

Lease Operating

Lease  operating  expense  increased  $9,000  during 1996 as compared  with 1995
primarily due to increased maintenance activity during 1996.




                                                        -7-

<PAGE>



Production Taxes

Production taxes increased $38,000 during 1996 as compared with 1995 as a result
of increased oil and gas production during 1996 as discussed above.

General and Administrative

General and  administrative  expenses  decreased  $9,000 during 1996 as compared
with 1995  primarily  due to a decrease in the  allocation  of overhead from the
general partner.

Depletion

Depletion  expense  increased $9,000 during 1996 as compared with 1995 due to an
increase in capitalized costs during 1996.

1995 Compared to 1994

Oil Revenue

Oil revenue decreased $37,000 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 40,675 barrels in 1994 to 35,169 barrels in 1995
is primarily due to decreased  state allowable  production  limits combined with
normal production declines.

Gas Revenue

Gas revenue  decreased  $286,000 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 435,640 mcf in 1994 to 353,904 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 $9,000 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 $3,000 during 1995 as compared with 1994 due to an
increase in capitalized costs during 1995.



                                                        -8-

<PAGE>



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 1984-3                                                                           12

    Balance Sheets at December 31, 1996 and 1995 -
       May Limited Partnership 1984-3                                                                            13

    Statements of Operations for the Years Ended
       December 31, 1996, 1995 and 1994 -
       May Limited Partnership 1984-3                                                                            14

    Statements of Changes in Partners'  Capital for the Years Ended December 31,
       1996, 1995 and 1994 -
       May Limited Partnership 1984-3                                                                            15

    Statements of Cash Flows for the Years Ended
       December 31, 1996, 1995 and 1994 -
       May Limited Partnership 1984-3                                                                            16

    Notes to Financial Statements - May Drilling Partnership 1984-3
       and May Limited Partnership 1984-3                                                                     17-20

SUPPLEMENTAL OIL AND GAS RESERVE INFORMATION (UNAUDITED)                                                         21

</TABLE>

                                                       -10-

<PAGE>



                                           INDEPENDENT AUDITORS' REPORT



To the Partners of May Drilling Partnership 1984-3 and
    May Limited Partnership 1984-3:

We have audited the  financial  statements  of May Drilling  Partnership  1984-3
("General   Partnership")   and  May  Limited   Partnership   1984-3   ("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 1984-3
                                                  BALANCE SHEETS
                                                  (In thousands)



                                                                      December 31,                December 31,
                                                                          1996                         1995

ASSETS
<S>                                                                       <C>                         <C> 
Investment in May Limited Partnership 1984-3                              $482                        $317
                                                                           ===                         ===


PARTNERS' CAPITAL
Partners' Capital                                                         $482                        $317
                                                                           ===                         ===






<FN>

Note:     The  statements of operations,  changes in partners'  capital and cash
          flows for May Drilling  Partnership  1984-3 are not presented  because
          such  information  is equal  to the  Limited  Partners'  share of such
          activity as presented in the May Limited  Partnership 1984-3 financial
          statements. The May Drilling Partnership carries its investment in May
          Limited  Partnership  1984-3 on the  equity  method.  The May  Limited
          Partnership 1984-3 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 1984-3
                                                  BALANCE SHEETS
                                                  (In thousands)



                                                                                 December 31,                December 31,
                                                                                     1996                         1995

ASSETS
CURRENT ASSETS
<S>                                                                                <C>                         <C>    
    Cash and cash equivalents                                                      $   390                     $   273
    Accrued oil and gas revenues                                                       367                         281
    Due from affiliate                                                                 132                          86
    Contributions receivable from general partner                                       36                          30
                                                                                   -------                      ------
          Total                                                                        925                         670
                                                                                    ------                      ------

OIL AND GAS PROPERTIES, using the
    full cost method of accounting                                                   7,641                       7,629
       Less accumulated depletion                                                  (7,641)                     (7,629)
                                                                                   ------                      ------
          Net oil and gas properties

TOTAL ASSETS                                                                      $    925                     $   670
                                                                                   =======                      ======

LIABILITIES AND PARTNERS' CAPITAL
CURRENT LIABILITIES
    Accounts payable and accrued liabilities                                     $      12                     $    16
                                                                                  --------                      ------

PARTNERS' CAPITAL
    General Partner                                                                    431                         337
    Limited Partner                                                                    482                         317
                                                                                   -------                      ------
          Total                                                                        913                         654
                                                                                   -------                      ------

TOTAL LIABILITIES AND PARTNERS' CAPITAL                                           $    925                     $   670
                                                                                   =======                      ======
















<FN>

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

                                                       -13-
</TABLE>

<PAGE>

<TABLE>
<CAPTION>


                                          MAY LIMITED PARTNERSHIP 1984-3
                                             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                                                   $    864                $   621              $    658
    Gas revenue                                                      1,422                    702                   988
    Interest income                                                     15                     15                    11
                                                                  --------                -------              --------
          Total                                                      2,301                  1,338                 1,657
                                                                    ------                 ------                ------

COSTS AND EXPENSES
    Lease operating                                                     38                     29                    26
    Production taxes                                                   143                    105                   114
    General and administrative                                          36                     45                    43
    Depletion                                                           12                      3
    Litigation settlement                                                                       8
    Professional services and other                                      9                      9                    12
                                                                  --------               --------              --------
          Total                                                        238                    199                   195
                                                                   -------                -------               -------

NET INCOME                                                         $ 2,063                $ 1,139               $ 1,462
                                                                    ======                 ======                ======

ALLOCATION OF NET INCOME:
    General Partner                                               $    696               $    382              $    486
                                                                   =======                =======               =======
    Limited Partner                                                $ 1,367               $    757              $    976
                                                                    ======                =======               =======
    Per initial $1,000 Limited Partner
       investment                                                  $207.15                $114.71               $147.90
                                                                    ======                 ======                ======
    Weighted average initial $1,000 Limited
       Partner investment units outstanding                          6,599                  6,599                 6,599
                                                                    ======                 ======               =======

















<FN>

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

                                                       -14-

<PAGE>

<TABLE>
<CAPTION>


                                          MAY LIMITED PARTNERSHIP 1984-3
                                    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                                          $  340                 $  333                $  673
    Capital contributions                                               29                                           29
    Net income                                                         486                    976                 1,462
    Distributions                                                     (523)                  (991)               (1,514)
                                                                     ------                 ------                ------

BALANCE, December 31, 1994                                             332                    318                   650
    Capital contributions                                               30                                           30
    Net income                                                         382                    757                 1,139
    Distributions                                                     (407)                  (758)               (1,165)
                                                                     ------                 ------                ------

BALANCE, December 31, 1995                                             337                    317                   654
    Capital contributions                                               36                                           36
    Net income                                                         696                  1,367                 2,063
    Distributions                                                     (638)                (1,202)               (1,840)
                                                                      -----                 ------                ------

BALANCE, December 31, 1996                                          $  431               $    482              $    913
                                                                     =====                =======               =======






















<FN>


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

                                                       -15-

<PAGE>

<TABLE>
<CAPTION>


                                          MAY LIMITED PARTNERSHIP 1984-3
                                             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                                                     $ 2,063                $ 1,139               $ 1,462
    Adjustment to reconcile net income
       to net cash provided by operating
       activities:
          Depletion                                                     12                      3
                                                                   -------               --------
             Cash from operations
                before working capital changes                       2,075                  1,142                 1,462

    Changes in assets and liabilities provided (used) cash:
       Accrued oil and gas revenues                                   (86)                   (49)                   116
       Due from affiliate                                             (46)                     13                  (40)
       Accounts payable and accrued
          liabilities                                                  (4)                      2                   (1)
                                                                 --------                --------             --------
             Net cash provided by
                operating activities                                 1,939                  1,108                 1,537
                                                                    ------                 ------                ------

INVESTING ACTIVITIES:
    Additions to oil and gas properties                               (12)                    (3)
                                                                  -------               --------

FINANCING ACTIVITIES:
    Distributions to partners                                      (1,840)                (1,165)               (1,514)
    Contributions from partners                                         30                     29                    26
                                                                   -------                -------              --------
             Net cash used in financing
                activities                                         (1,810)                (1,136)               (1,488)
                                                                   ------                 ------                ------

NET INCREASE (DECREASE) IN CASH
    AND CASH EQUIVALENTS                                               117                   (31)                    49

CASH AND CASH EQUIVALENTS:

    BEGINNING OF YEAR                                                  273                    304                   255
                                                                   -------                -------               -------

    END OF YEAR                                                   $    390               $    273              $    304
                                                                   =======                =======               =======





<FN>

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


                                                       -16-

<PAGE>



                                         MAY DRILLING PARTNERSHIP 1984-3
                                                        AND
                                          MAY LIMITED PARTNERSHIP 1984-3

                                           NOTES TO FINANCIAL STATEMENTS


(1)    ACCOUNTING POLICIES AND OTHER MATTERS

          General Partnership

          May Drilling  Partnership  1984-3,  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   1984-3   (the   "Limited   Partnership").   The  General
          Partnership   was  formed  on   November  7,  1984,   with   investors
          ("Participants")  subscribing an aggregate of $6,599,000 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  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                            66.4%              66.7%              66.9%
General Partner                            33.6%              33.3%              33.1%
</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%
TKG 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.

          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.


                                                       -18-

<PAGE>



          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 $132,000 and $86,000 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, $45,000 in 1995 and
          $43,000 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  $8,000 and
          $6,600, 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 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 $8,000.

                                                       -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.
<TABLE>
<CAPTION>

Costs Incurred -


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

<S>                                                           <C>                    <C>                   <C>
Development costs                                             $12                    $ 3                   $
                                                               ==                     ==                    ==
</TABLE>
<TABLE>
<CAPTION>

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


                                                           1996                            1995                            1994
                                                          ------                          ------                          -----
                                              Bbls            Mcf             Bbls            Mcf             Bbls            Mcf
                                                                     (In thousands)

Total Proved Reserves:
<S>                                             <C>            <C>              <C>            <C>              <C>            <C>
    Beginning of period                         39             383              36             320              29             259
    Revisions to previous estimates             38             464              38             417              48             497
    Production                                (40)           (452)            (35)           (354)            (41)           (436)
                                              ---            ----             ---            ----             ---            ----
       End of Period                            37             395              39             383              36             320
                                               ===            ====             ===            ====             ===            ====

Proved Developed Reserves:
       Beginning of period                      39             383              36             320              29             259
                                               ===            ====             ===            ====             ===            ====
       End of period                            37             395              39             383              36             320
                                               ===            ====             ===            ====             ===            ====
</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 37.8% 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. 
                   2-89194, 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 1984-3
                        MAY LIMITED PARTNERSHIP 1984-3
                        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\MAY84-3K.DOC
                                                       -23-

<PAGE>