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

                   For the Fiscal Year Ended December 31, 1998

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

                         Commission File Number 2-89194


                         MAY DRILLING PARTNERSHIP 1984-1
                         MAY LIMITED PARTNERSHIP 1984-1
             (Exact name of registrant as specified in its charter)


                                                                      75-1973664
                    Texas                                             75-1973661
         (State or other jurisdiction of                        (I.R.S. Employer
         incorporation or organization)                   Identification Number)

    4582 South Ulster Street Parkway
              Suite 1700
          Denver, Colorado                                                 80237
(Address of principal executive offices)                              (Zip Code)

       Registrant's telephone number, including area code: (303) 850-7373

           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>


                      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



<PAGE>


                                     PART I


ITEM 1 - BUSINESS

May Drilling Partnership 1984-1 (the "Drilling or General  Partnership") and May
Limited  Partnership  1984-1 (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
1999, HPI employed 122 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, 1998, all such required  contributions had been
made.

The partnership  agreements  governing the Drilling  Partnership and the Limited
Partnership provide for a fifteen-year term of existence.  As a result, the term
of the Drilling Partnership and the Limited Partnership will be through July 18,
1999.

The  Limited  Partnership  will be wound up after it  terminates  in 1999.  This
process  includes  preparing a final  accounting,  paying the liabilities of the
Drilling  Partnership  and the  Limited  Partnership,  and making a  liquidating
distribution  in  accordance  with the  capital  accounts of the  partners.  The
general  partner  believes that it would be in the best interest of the partners
to sell the assets of the Limited  Partnership and distribute any cash remaining
after payment of  liabilities.  The  distribution  of a pro rata direct  working
interest in the Freddie Aker well to each of the partners  would not be feasible
because of the large number of partners  involved  (over 700), the small size of
the resulting interests and, in general, the risks and inconvenience that can be
associated  with being a small working  interest  owner.  The general partner is
considering the alternatives available for the sale of the partnership's assets.
The general partner plans to submit to the partners for approval an amendment to
the partnership agreements which would permit the Partnerships to sell their oil
and gas property to the general partner. In order to maximize the value realized
by the Limited  Partnership  from the sale of its primary asset, its interest in
the  Freddie  Aker well,  the  general  partner is  considering  soliciting  the
partners'  consent to commence the  termination  process for the  partnership in
July 1999.

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.


<PAGE>

<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:



<PAGE>


                                      1998              1997             1996
                                      ----              ----             ----

Limited Partner                       62.7%             62.7%            62.9%
General Partner                       37.3%             37.3%            37.1%

In 1999, the sharing ratio will be 62.6% to the limited partner and 37.4% to the
general partner.

To  the  extent  that  the  characterization  of  any  expense  to  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.

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, 1998, 1997 and 1996, purchases by the following
companies  exceeded  10% of the  total  oil  and  gas  revenues  of the  Limited
Partnership:

                                       1998              1997             1996
                                       ----              ----             ----

Conoco Inc.                             48%              41%               56%
Marathon Petroleum Company              16%              39%
TXG Gas Marketing                       17%              19%               30%
Scurlock Permian LLC                    17%

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  Limited  Partnership's  historical
environmental  expenditures  have not been  material  and are not expected to be
material in the future. The general partner is continually taking all actions it
believes  necessary  in its  operations  to ensure  conformity  with  applicable
federal,  state  and  local  environmental  regulations  and does not  presently
anticipate  that  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.



<PAGE>


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.

Issues Related to the Year 2000

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

General.  The following  Year 2000  statements  constitute a Year 2000 Readiness
Disclosure  within  the  meaning  of the Year  2000  Information  and  Readiness
Disclosure  Act of 1998.  The Year 2000 problem has arisen because many existing
computer  programs  use only the last two digits to refer to a year.  Therefore,
these  computer  programs do not properly  recognize and process date  sensitive
information  beyond  1999.  In  general,  there  are two areas  where  Year 2000
problems may exist for the Limited Partnership:  information  technology such as
computers,  programs and related systems ("IT") and  non-information  technology
systems such as embedded technology on a silicon chip ("Non IT").

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

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

With regard to the Limited Partnership's Non IT systems, the Limited Partnership
believes that most of these systems can be brought into  compliance on schedule.
The  Limited  Partnership's  assessment  of  third  party  readiness  is not yet
completed.  Because  Non IT systems  are  embedded  chips,  it is  difficult  to
determine with complete accuracy where all such systems are located.  As part of
its Plan, the Limited Partnership is making formal and informal inquiries of its
vendors,  customers and  transporters  in an effort to determine the third party
systems that might have embedded technology requiring remediation.

Estimated  Costs.  Although  it is  difficult  to  estimate  the total  costs of
implementing  the  Plan  through  January  1,  2000  and  beyond,   the  Limited
Partnership's  preliminary  estimate  is that such costs  will not be  material.
However,  although management believes that its estimates are reasonable,  there
can be no  assurance,  for the reasons  stated in the next  paragraph,  that the
actual  cost of  implementing  the Plan  will  not  differ  materially  from the
estimated costs.

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

Cautionary Statement Regarding Forward-Looking Statements

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


ITEM 2 - PROPERTIES

The Limited  Partnership's  oil and gas  reserves are located on  properties  in
south Louisiana. Natural gas accounts for 74% of estimated future gross revenues
in the Limited Partnership's reserve report as of December 31, 1998.

Significant Properties

At December 31, 1998, the following  properties accounted for all of the Limited
Partnership's proved oil and gas reserves. Reserve quantities were obtained from
the December 31, 1998 reserve report prepared by HPI's petroleum engineers.

Meaux Prospect.  The Meaux 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 6,000 bbls
of oil and 69,000 mcf of gas as of December 31, 1998. The Limited  Partnership's
working interest in this well is 8.7%. The prospect  produces from one zone, the
Bol Mex 3 formation, at 15,275 feet.

As part of the  liquidation  process,  the general  partner is  considering  the
alternatives  available  for the  sale of the  Limited  Partnership's  property,
including a sale of the  property at public  auction.  The general  partner also
plans to submit to the partners  for  approval an  amendment to the  partnership
agreements  which would permit the Limited  Partnership  to sell its oil and gas
property  to the  general  partner,  either at a public  auction or in a private
sale.




<PAGE>


ITEM 3 - LEGAL PROCEEDINGS

None.


ITEM 4 - SUBMISSION OF MATTERS TO A VOTE OF STOCKHOLDERS

No matter was submitted to a vote of  participants  during the fourth quarter of
1998.



                                     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, 1998, there were  approximately 487 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

1998                          $ 192                      $ 324
1997                            308                        519
1996                            380                        646


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

                                                            For the Limited Partnership
                                                     As of or for the Year Ended December 31,
                                                     ----------------------------------------
                                    1998              1997             1996              1995             1994
                                    ----              ----             ----              ----             ----
                                                                  (In thousands)

<S>                                <C>               <C>              <C>               <C>              <C>   
Total revenues                     $  387            $  867           $1,329            $  774           $  956
Oil and gas revenues                  378               850            1,318               763              949
Net income                            286               713            1,174               637              822
Working capital                       197               406              541               393              394
Total assets                          260               439              552               408              406
Partners' capital                      --               427              541               393              394
Net assets in liquidation             197                --               --                --               --
</TABLE>



<PAGE>


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

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

Appreciation of oil and gas properties                    $  52
Deferral of appreciated gain on oil and gas properties       (52)

Liquidity and Capital Resources

Material changes in the Limited  Partnership's cash position for the years ended
December 31, 1998 and 1997 are summarized as follows:

                                                    1998              1997
                                                    ----              ----
                                 (In thousands)

Cash provided by operating activities              $  435            $  831
Distributions to partners                            (516)             (827)
Additions to oil and gas properties                                     (48)
                                                  -------             -----
Increase (decrease) in cash                        $  (81)           $  (44)
                                                    =====             =====

Cash  provided  by  operating   activities  in  1998  was  used   primarily  for
distributions to the partners.  A distribution  payable to partners of record as
of December 31, 1998 was declared in January 1999.  The  distribution  amount is
$59,000, payable $36,993 to the Drilling Partnership partners and $22,007 to the
general partner. 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 $197,000 at December  31,
1998. 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) from proved
reserves were  estimated at 6,000 bbls and 69,000 mcf valued at $193,000 in 1998
and 18,000 bbls and 191,000  mcf valued at  $744,000  in 1997.  The  decrease in
discounted future net revenues and the decrease in the quantities  resulted from
a decrease in year-end oil and gas prices,  as well as current  year  production
and a decrease in the  estimated  rate of future  production on the Freddie Aker
well as it is nearing the end of its  productive  life.  Estimates of discounted
future net revenues  should not be construed as the current  market value of the
estimated  oil  and  gas  reserves.  In  accordance  with  requirements  of  the
Securities and Exchange Commission, the estimated discounted future net revenues
from proved  reserves are generally  based on prices and costs as of the date of
the estimate, whereas actual future prices and costs may be materially higher or
lower. In addition,  the 10% discount  factor,  which is required by the SEC for
reporting  purposes,  is not  necessarily the most  appropriate  discount factor
based on risks associated with the production of the reserves or the oil and gas
industry in general.  Accordingly,  the price  received from the sale of oil and
gas reserves is not generally the same as the estimated  future net revenues for
those reserves and the amount received in liquidation of the assets.

Recently Issued Accounting Pronouncements

In June 1997,  the  Financial  Accounting  Standards  Board issued  Statement of
Financial Accounting Standards No. 130 "Reporting  Comprehensive  Income" ("SFAS
130"). SFAS 130 establishes standards for reporting and display of comprehensive
income and its components (revenues,  expenses, gains, and losses) in a full set
of general purpose financial  statements.  SFAS 130 requires that all items that
are  required to be  recognized  under  accounting  standards as  components  of
comprehensive income be reported in a financial statement that is displayed with
the same prominence as other financial statements. Reclassification of financial
statements for earlier periods  provided for  comparative  purposes is required.
The  Limited  Partnership  adopted  SFAS 130 on  January 1,  1998.  The  Limited
Partnership does not have any items of other comprehensive  income for the years
ended December 31, 1998, 1997 and 1996. Therefore, total comprehensive income is
the same as net income for those periods.

In June 1997,  the  Financial  Accounting  Standards  Board issued  Statement of
Financial  Accounting  Standards  No.  131  "Disclosures  about  Segments  of an
Enterprise and Related Information" ("SFAS 131"). SFAS 131 establishes standards
for  reporting  selected   information  about  operating  segments  and  related
disclosures about products and services,  geographic areas, and major customers.
SFAS 131 requires that an entity report  financial and  descriptive  information
about  its  operating  segments  which  are  regularly  evaluated  by the  chief
operating  decision maker in deciding how to allocate resources and in assessing
performance. The Limited Partnership adopted SFAS 131 in 1998.

The Limited Partnership  engages in the development,  production and sale of oil
and gas, and the acquisition,  exploration, development and operation of oil and
gas  properties in the  continental  United  States.  These  activities  exhibit
similar  economic  characteristics  and  involve the same  products,  production
processes,  class of customers,  and methods of distribution.  Management of the
Limited Partnership  evaluates its performance as a whole rather than by product
or geographically.  As a result, the Limited Partnership's operations consist of
one reportable segment.

Results of Operations

1998 Compared to 1997

Gas Revenue

Gas revenue  decreased  $269,000 during 1998 compared with 1997. The decrease is
due to a decrease  in the  average  gas price from $3.07 per mcf during  1997 to
$2.50 per mcf during  1998,  combined  with a 40%  decrease in  production.  The
decrease in production from 170,665 mcf in 1997 to 102,011 mcf in 1998 is due to
increased rates of water production on the Freddie Aker #1 well in Louisiana.

Oil Revenue

Oil revenue  decreased  $203,000 during 1998 compared with 1997. The decrease is
comprised  of a 41%  decrease  in  production,  combined  with a decrease in the
average  price  from to $20.28  per barrel in 1997 to $12.99 per barrel in 1998.
The decrease in production  from 16,079 barrels in 1997 to 9,486 barrels in 1998
is due to  increased  rates of water  production  on the Freddie Aker #1 well in
Louisiana.

Interest Income

Interest income  decreased  $2,000 during 1998 compared with 1997 due to a lower
average cash balance during 1998.

Other

Other income  during 1997  comprised of insurance  proceeds  which  reimbursed a
portion of expense incurred in a prior period to settle certain litigation.

Lease Operating

Lease  operating  expense  decreased  $9,000  during  1998  compared  with  1997
primarily due to decreased maintenance activity during 1998.




<PAGE>


Production Taxes

Production taxes decreased $30,000 during 1998 compared with 1997 as a result of
a decreased oil and gas production during 1998.

General and Administrative

General and  administrative  expense  increased $1,000 during 1998 compared with
1997 primarily due to an increase in performance based compensation expense.

Depletion

Depletion  expense  decreased  $15,000  during 1998  compared with 1997 due to a
decrease in the depletion rate,  caused by the decrease in production  discussed
above, and lower capitalized costs during 1998.

1997 Compared to 1996

Gas Revenue

Gas revenue  decreased  $296,000 during 1997 compared with 1996. The decrease is
due to a decrease  in the  average  gas price from $3.15 per mcf during  1996 to
$3.07 per mcf during  1997  combined  with a 34%  decrease  in  production.  The
decrease in production from 260,436 mcf in 1996 to 170,665 mcf in 1997 is due to
normal production declines.

Oil Revenue

Oil revenue  decreased  $172,000 during 1997 as compared with 1996. The decrease
is comprised of a 31% decrease in  production,  combined  with a decrease in the
average  price  from to $24.40  per barrel in 1996 to $20.28 per barrel in 1997.
The decrease in production from 23,270 barrels in 1996 to 16,079 barrels in 1997
is due to normal production declines.

Other

Other income is comprised of insurance  proceeds  which  reimbursed a portion of
expense incurred in a prior period to settle certain litigation.

Lease Operating

Lease  operating  expense  increased  $8,000  during 1997 as compared  with 1996
primarily due to increased maintenance activity during 1997.

Production Taxes

Production taxes decreased $26,000 during 1997 as compared with 1996 as a result
of a decreased oil and gas production during 1997 as discussed above.

General and Administrative

General and administrative  expenses decreased $3,000 during 1997 as compared to
1996  primarily due to a decrease in the allocation of overhead from the general
partner.

Depletion

Depletion  expense increased $20,000 during 1997 as compared with 1996 due to an
increase in capitalized costs during 1997.



<PAGE>


ITEM 7A - QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

The Limited  Partnership's  primary market risk relates to changes in the prices
received from sales of oil and natural gas production.  The Limited  Partnership
manages  its  commodity  price  risks  by  using  well-trained  and  experienced
marketing personnel to sell its production. The Limited Partnership does not use
any financial  instruments or derivative commodity  instruments that are subject
to price or interest rate risk.


<PAGE>


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

                                           INDEX TO FINANCIAL STATEMENTS


                                                                                                               Page

FINANCIAL STATEMENTS:

<S>                                                                                                              <C>
   Independent Auditors' Report                                                                                  14

   Statement of Net Assets in Liquidation at December 31, 1998 and Balance Sheet
     at December 31, 1997 -
     May Drilling Partnership 1984-1                                                                             15

   Statement of Net Assets in Liquidation at December 31, 1998 and Balance Sheet
     at December 31, 1997 -
     May Limited Partnership 1984-1                                                                              16

   Statements of Operations for the Years Ended
     December 31, 1998, 1997 and 1996 -
     May Limited Partnership 1984-1                                                                              17

   Statement of Changes in Net Assets in Liquidation for the Year Ended December
     31, 1998 and Statements of Changes in Partners' Capital for the Years Ended
     December 31, 1997 and 1996 -
     May Limited Partnership 1984-1                                                                              18

   Statements of Cash Flows for the Years Ended
     December 31, 1998, 1997 and 1996 -
     May Limited Partnership 1984-1                                                                              19

   Notes to Financial Statements - May Drilling Partnership 1984-1
     and May Limited Partnership 1984-1                                                                       20-24

SUPPLEMENTAL OIL AND GAS RESERVE INFORMATION (UNAUDITED)                                                         25

</TABLE>

<PAGE>


                          INDEPENDENT AUDITORS' REPORT



To the Partners of May Drilling Partnership 1984-1 and
   May Limited Partnership 1984-1:

We  have  audited  the  accompanying   financial   statements  of  May  Drilling
Partnership  1984-1 ("General  Partnership") and May Limited  Partnership 1984-1
("Limited  Partnership")  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.

As discussed in Note 1 to the financial statements, the terms of the partnership
agreements governing the General Partnership and the Limited Partnership provide
for a fifteen year term of existence  which extends  through July 18, 1999.  The
partnerships  are expected to be liquidated  in 1999.  As a result,  the General
Partnership and the Limited  Partnership  have changed their basis of accounting
from the going concern basis to the  liquidation  basis  effective  December 31,
1998.

In our  opinion,  such  financial  statements  present  fairly,  in all material
respects,  (1) the net assets in liquidation of the General  Partnership and the
Limited  Partnership  as of December 31, 1998,  (2) the changes in net assets in
liquidation of the Limited Partnership for the year ended December 31, 1998, (3)
the financial position of the General Partnership and the Limited Partnership at
December  31,  1997,  and (4) the results of  operations  and cash flows of the
Limited Partnership for each of the three years in the period ended December 31,
1998 in conformity with generally  accepted  accounting  principles on the bases
described in the preceding paragraph.



DELOITTE & TOUCHE LLP

Denver, Colorado
March 29, 1999



<PAGE>

<TABLE>
<CAPTION>

                                          MAY DRILLING PARTNERSHIP 1984-1
                                      STATEMENT OF NET ASSETS IN LIQUIDATION
                                      AT DECEMBER 31, 1998 AND BALANCE SHEET
                                               AT DECEMBER 31, 1997
                                                  (In thousands)



                                                                          1998                      1997
                                                                     --------------            ---------

ASSETS
<S>                                                                      <C>                       <C> 
Investment in May Limited Partnership 1984-1                              $ 40                      $188
                                                                           ===                       ===


PARTNERS' CAPITAL
Partners' Capital                                                                                   $188

NET ASSETS IN LIQUIDATION                                                 $ 40
                                                                           ===






<FN>

Note:  The  statements  of  operations,  changes in net  assets in  liquidation,
changes in partners' capital and cash flows for May Drilling  Partnership 1984-1
are not presented  because such  information  is equal to the Limited  Partner's
share of such  activity  as  presented  in the May  Limited  Partnership  1984-1
financial statements. The May Drilling Partnership carries its investment in May
Limited  Partnership  1984-1 on the equity method.  The May Limited  Partnership
1984-1  financial  statements  should be read in  conjunction  with this balance
sheet. The May Limited  Partnership  1984-1 changed its basis of accounting from
the going concern basis to the liquidation basis effective  December 31, 1998 as
described in Note 1 to the financial statements.

</FN>




















<FN>


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

                         MAY LIMITED PARTNERSHIP 1984-1
                     STATEMENT OF NET ASSETS IN LIQUIDATION
                     AT DECEMBER 31, 1998 AND BALANCE SHEET
                              AT DECEMBER 31, 1997
                                 (In thousands)


                                                                          1998                      1997
                                                                     --------------            ---------

ASSETS
<S>                                                                    <C>                        <C>     
  Cash and cash equivalents                                            $    140                   $    221
  Accrued oil and gas revenues                                               40                        127
  Due from affiliate                                                         19                         70

OIL AND GAS PROPERTIES:
  At estimated net realizable value                                          61
  Using the full cost method of accounting
     less accumulated depletion of $8,091                                                               21
                                                                     ----------                   --------

TOTAL ASSETS                                                                260                   $    439
                                                                        -------                    =======

LIABILITIES
  Accounts payable and accrued liabilities                                   11                  $      12
  Deferred appreciated gain on oil and gas properties                        52                 
                                                                       --------

PARTNERS' CAPITAL
  General partner                                                                                      239
  Limited partner                                                                                      188
         Total                                                                                         427

TOTAL LIABILITIES AND PARTNERS' CAPITAL                                                           $    439
                                                                                                   =======

NET ASSETS IN LIQUIDATION                                              $    197
                                                                        =======





















<FN>

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

                         MAY LIMITED PARTNERSHIP 1984-1
                            STATEMENTS OF OPERATIONS
                 FOR THE YEARS ENDED DECEMBER 31, 1998, 1997 AND 1996
                 (In thousands, except for Unit and per Unit
                                  Information)


                                                                      1998             1997              1996
                                                                      ----             ----              ----

REVENUES
<S>                                                               <C>              <C>                <C>     
  Gas revenue                                                     $     255        $     524          $    820
  Oil revenue                                                           123              326               498
  Interest income                                                         9               11                11
  Other                                                                                    6       
                                                                -----------       ----------
         Total                                                          387              867             1,329
                                                                   --------          -------            ------

COSTS AND EXPENSES
  Lease operating                                                        21               30                22
  Production taxes                                                       26               56                82
  General and administrative                                             32               31                34
  Depletion                                                              12               27                 7
  Professional services and other                                        10               10                10
                                                                  ---------        ---------         ---------
         Total                                                          101              154               155
                                                                   --------          -------           -------

NET INCOME                                                        $     286         $    713           $ 1,174
                                                                   ========          =======            ======

ALLOCATION OF NET INCOME:
  General Partner                                                 $     110         $    273         $     438
                                                                   ========          =======          ========
  Limited Partner                                                 $     176         $    440         $     736
                                                                   ========          =======          ========
  Per initial $1,000 Limited Partner investment                     $ 32.77          $ 81.92           $137.03
                                                                     ======           ======            ======
  Weighted average initial $1,000 Limited
     Partner investment units outstanding                             5,371            5,371             5,371
                                                                     ======           ======            ======























<FN>

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

                         MAY LIMITED PARTNERSHIP 1984-1
                STATEMENT OF CHANGES IN NET ASSETS IN LIQUIDATION
                    FOR THE YEAR ENDED DECEMBER 31, 1998 AND
                   STATEMENTS OF CHANGES IN PARTNERS' CAPITAL
                 FOR THE YEARS ENDED DECEMBER 31, 1997 AND 1996
                                 (In thousands)


                                                                                             Net Assets
                                                           General           Limited             in
                                                           Partner           Partner        Liquidation          Total

<S>                                                        <C>              <C>                                <C>   
BALANCE, December 31, 1995                                  $  216           $  177                             $  393
  Net income                                                   438              736                              1,174
  Distributions                                              (380)            (646)                            (1,026)
                                                            -----            -----                             ------

BALANCE, December 31, 1996                                     274              267                                541
  Net income                                                   273              440                                713
  Distributions                                              (308)            (519)                              (827)
                                                            -----            -----                              -----

BALANCE, December 31, 1997                                     239              188                                427
  Net income                                                   110              176                                286
  Distributions                                              (192)            (324)                              (516)

  Adjustments to liquidation basis:
    Eliminate Partners' Capital                              (157)             (40)                              (197)
    Revaluation of assets and liabilities                                                       $ 197              197
                                                           -------          -------              ----            -----

BALANCE, December 31, 1998                                  $  -0-           $  -0-             $ 197           $  197
                                                             =====            =====              ====            =====

























<FN>

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

                         MAY LIMITED PARTNERSHIP 1984-1
                                             STATEMENTS OF CASH FLOWS
                               FOR THE YEARS ENDED DECEMBER 31, 1998, 1997 AND 1996
                                                  (In thousands)


                                                                      1998             1997              1996
                                                                      ----             ----              ----

OPERATING ACTIVITIES:
<S>                                                                 <C>              <C>               <C>    
  Net income                                                        $   286          $   713           $ 1,174
  Adjustment to reconcile net income
     to net cash provided by operating activities:
       Depletion                                                         12               27                 7

  Changes in assets and liabilities provided (used) cash:
       Accrued oil and gas revenues                                      87               85               (50)
       Due from affiliate                                                51                5               (26)
       Accounts payable and accrued liabilities                          (1)               1                (4)
                                                                   --------         --------         ---------
         Net cash provided by operating activities                      435              831             1,101
                                                                     ------           ------            ------

INVESTING ACTIVITIES -
  Additions to gas and oil properties                                                    (48)               (7)
                                                                 ----------           ------         ---------

FINANCING ACTIVITIES -
  Distributions to partners                                            (516)            (827)           (1,026)
                                                                     ------           ------            ------

NET INCREASE (DECREASE) IN CASH AND
  CASH EQUIVALENTS                                                      (81)             (44)               68

CASH AND CASH EQUIVALENTS:

  BEGINNING OF YEAR                                                     221              265               197
                                                                     ------           ------            ------

  END OF YEAR                                                       $   140          $   221           $   265
                                                                     ======           ======            ======



















<FN>

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

                         MAY DRILLING PARTNERSHIP 1984-1
                                       AND
                         MAY LIMITED PARTNERSHIP 1984-1

                          NOTES TO FINANCIAL STATEMENTS


(1)      ACCOUNTING POLICIES AND OTHER MATTERS

       General Partnership

       May  Drilling  Partnership  1984-1,  a  Texas  general  partnership  (the
       "General  Partnership"),  was organized by May Petroleum Inc. ("May") for
       the purposes of oil and gas exploration  through May Limited  Partnership
       1984-1 (the "Limited Partnership"). The General Partnership was formed on
       July 18, 1984, with investors  ("Participants")  subscribing an aggregate
       of $5,371,000 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 15% 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 all years since 1989 and intends to make a repurchase offer in 1999.

       As the General  Partnership  is the sole  limited  partner of the Limited
       Partnership,  and there are no other  revenues or expenses of the General
       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 net assets in  liquidation,  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 located in
       prospects  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.  At December 31,  1998,  no  additional
       contributions were necessary to comply with this requirement.

       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.


<PAGE>


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

Appreciation of oil and gas properties                    $  52
Deferral of appreciated gain on oil and gas properties       (52)

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

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

       The balance sheet of the General  Partnership and the Limited Partnership
       as of December 31, 1997 and the related  statements  of  operations,  and
       cash flows of the Limited  Partnership for each of the three years in the
       period ended  December 31, 1998 and the  statements of partners'  capital
       for the years ended  December 31, 1997 and 1996 have been prepared  using
       the  historical  cost (going  concern)  basis of  accounting on which the
       General  Partnership and the Limited  Partnership had previously reported
       their financial condition and results of operations.

       The Limited  Partnership  will be wound up after it  terminates  in 1999.
       This  process  includes   preparing  a  final   accounting,   paying  the
       liabilities of the Drilling Partnership and the Limited Partnership,  and
       making a liquidating distribution in accordance with the capital accounts
       of the  partners.  The general  partner  believes that it would be in the
       best  interest  of the  partners  to  sell  the  assets  of  the  Limited
       Partnership   and  distribute   any  cash  remaining   after  payment  of
       liabilities.   The  general  partner  is  considering  the   alternatives
       available for the sale of the partnership's  assets.  The general partner
       plans  to  submit  to the  partners  for  approval  an  amendment  to the
       partnership  agreements which would permit the Partnerships to sell their
       oil and gas properties to the general  partner.  In order to maximize the
       value  realized by the Limited  Partnership  from the sale of its primary
       asset,  its  interest in the Freddie  Aker well,  the general  partner is
       considering  soliciting the partners' consent to commence the termination
       process for the partnership in July 1999.

       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:

                                       1998              1997             1996
                                       ----              ----             ----

Limited Partner                        62.7%            62.7%             62.9%
General Partner                        37.3%            37.3%             37.1%



<PAGE>


       Significant Customers

       For the years ended  December 31, 1998,  1997 and 1996,  purchases by the
       following companies exceeded 10% of the total oil and gas revenues of the
       Limited Partnership:

                                       1998              1997             1996
                                       ----              ----             ----

Conoco Inc.                             48%              41%               56%
Marathon Petroleum Company              16%              39%
TXG Gas Marketing                       17%              19%               30%
Schurlock Permian LLC                   17%

       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

       Prior to December 31,  1998,  the Limited  Partnership  followed the full
       cost method of accounting  for oil and gas properties  and,  accordingly,
       capitalized 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 $.03 in 1998, $.03 in 1997 and $.01 in 1996.

       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 1998, 1997 or 1996.  Significant price declines in the future
       could cause the Limited  Partnership to recognize  valuation  adjustments
       and  could  reduce  the  amount  of  future  cash  flow   available   for
       distributions and operations.

       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 of  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, 1998, the Limited Partnership had a net under-produced
       position  which was not  considered  material.  On December 31, 1998, the
       Limited Partnership adopted the liquidation basis of accounting.  The net
       gas  imbalance at December 31, 1998 has not been  assigned a value as the
       Limited  Partnership  does not anticipate  collection of these immaterial
       imbalances.



<PAGE>


       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  $19,000 as of December 31, 1998 and $70,000 as
       of December 31, 1997. These balances represent net revenue 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.

       Recently Issued Accounting Pronouncements

       In June 1997, the Financial  Accounting  Standards Board issued Statement
       of  Financial  Accounting  Standards  No.  130  "Reporting  Comprehensive
       Income" ("SFAS 130").  SFAS 130  establishes  standards for reporting and
       display of comprehensive income and its components  (revenues,  expenses,
       gains, and losses) in a full set of general purpose financial statements.
       SFAS 130 requires that all items that are required to be recognized under
       accounting standards as components of comprehensive income be reported in
       a financial statement that is displayed with the same prominence as other
       financial  statements.   Reclassification  of  financial  statements  for
       earlier  periods  provided  for  comparative  purposes is  required.  The
       Limited  Partnership  adopted  SFAS 130 on January 1, 1998.  The  Limited
       Partnership does not have any items of other comprehensive income for the
       years  ended  December  31,  1998,  1997  and  1996.   Therefore,   total
       comprehensive income is the same as net income for those periods.

       In June 1997, the Financial  Accounting  Standards Board issued Statement
       of Financial  Accounting Standards No. 131 "Disclosures about Segments of
       an Enterprise and Related Information" ("SFAS 131"). SFAS 131 establishes
       standards for reporting selected information about operating segments and
       related  disclosures  about products and services,  geographic areas, and
       major  customers.  SFAS 131 requires that an entity report  financial and
       descriptive  information about its operating segments which are regularly
       evaluated  by the  chief  operating  decision  maker in  deciding  how to
       allocate resources and in assessing performance.
       The Limited Partnership adopted SFAS 131 in 1998.

       The Limited Partnership  engages in the development,  production and sale
       of oil  and  gas,  and  the  acquisition,  exploration,  development  and
       operation of oil and gas  properties in the  continental  United  States.
       These activities exhibit similar economic characteristics and involve the
       same products,  production processes,  class of customers, and methods of
       distribution.   Management  of  the  Limited  Partnership  evaluates  its
       performance  as a whole  rather than by product or  geographically.  As a
       result,  the Limited  Partnership's  operations consist of one reportable
       segment.



<PAGE>



(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 $27,000 in 1998, $31,000 in 1997 and $34,000 in 1996.


(3)      INCOME TAXES

       As a result of differences  between the  accounting  treatment of certain
       items for income tax purposes and 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, 1998 and
       1997 the  income  tax  bases  of the  Limited  Partnership's  oil and gas
       properties were approximately $600 and $1,600, respectively.




<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 Year Ended December 31,
                                 1998 1997 1996
                                 (In thousands)

<S>                                        <C>               <C>              <C> 
Development costs                          $  -              $ 48             $  7
                                            ===               ===              ===
</TABLE>

Oil and Gas Reserves (valued at year-end prices discounted at 10%) -
<TABLE>
<CAPTION>

                                               1998                    1997                     1996
                                               ----                    ----                     ----
                                         Mcf         Bbls        Mcf         Bbls         Mcf         Bbls
                                                                  (In thousands)

Total Proved Reserves:
<S>                                        <C>          <C>        <C>           <C>        <C>          <C>
   Beginning of period                     191          18         228           22         221          23
   Revisions to previous
     estimates                             (20)         (3)        134           12         267          22
   Production                             (102)         (9)       (171)        (16)        (260)        (23)
                                         -----        ----        ----       -----         ----       -----
          End of Period                     69           6         191           18         228          22
                                        ======        ====        ====        =====        ====       =====

Proved Developed Reserves:
   Beginning of period                     191          18         228           22         221          23
                                         =====        ====        ====        =====        ====       =====
   End of period                            69           6         191           18         228          22
                                        ======       =====        ====        =====        ====       =====
</TABLE>

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


<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   35.8%  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.
27  Financial Data Schedule


<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 1984-1
                                        MAY LIMITED PARTNERSHIP 1984-1

                                        By:  EDP OPERATING, LTD.,
                                             General Partner

                                             By:  HEPGP LTD.,
                                                  General Partner

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



Date:  March 29, 1999                        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/Thomas J. Jung                Vice President                   March 29, 1999
Thomas J. Jung            (Principal Accounting Officer)