SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC. 20549

                                    FORM 10-Q

                   QUARTERLY REPORT UNDER SECTION 13 or 15 (d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934




For Quarter Ended June 30, 1998                   Commission file number 0-10697



                            DORCHESTER HUGOTON, LTD.
             (Exact name of registrant as specified in its charter)




              Texas                                     75-1829064
(State or other jurisdiction of           (I.R.S. Employer Identification No.)
 Incorporation or organization)



        1919 S. Shiloh Road, Suite 600 - LB 48, Garland, Texas 75042-8234
               (Address of principal executive offices) (Zip Code)


       Registrant's telephone number, including area code: (972) 864-8610


                                      None
                  Former name, former address and former fiscal
                       year, if changed since last report


     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

     As of July 31, 1998,  10,744,380  Depositary  Receipts for Units of Limited
Partnership Interest were outstanding.


<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)

                          QUARTERLY REPORT ON FORM 10-Q

                                  June 30, 1998


                                      INDEX


PART I.   FINANCIAL INFORMATION

  Item 1. Financial Statements:

          Condensed Balance Sheets as of June 30, 1998 and
          December 31, 1997 (Unaudited)

          Condensed Statements of Earnings for the Three and Six
          Months Ended June 30, 1998 and 1997 (Unaudited)

          Condensed Statements of Cash Flows for the Six Months Ended
          June 30, 1998 and 1997 (Unaudited)

          Notes to Condensed Financial Statements (Unaudited)


  Item 2. Management's Discussion and Analysis of Financial Condition and
          Results of Operations



PART II.  OTHER INFORMATION

  Item 1. Legal Proceedings

  Item 5. Other Information

  Item 6. Exhibits and Reports on Form 8-K



SIGNATURES



<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)
PART I
Item 1
                            CONDENSED BALANCE SHEETS
                                   (Unaudited)

                       June 30, 1998 and December 31, 1997
                            (In Thousands of Dollars)

                                                           June 30,   Dec. 31,
                                                             1998       1997
                                                           --------   --------
                                     ASSETS
Current assets:
    Cash and cash equivalents .......................      $  3,583    $ 3,344
    Restricted cash ..................................          370        -0-
    Investments - available for sale .................        4,568      3,304
    Accounts receivable, net .........................        1,488      2,086
    Prepaid expenses and other current assets ........          191        136
                                                            -------    -------
      Total current assets ...........................       10,200      8,870

Property and Equipment - at cost .....................       28,299     27,875
    Less depreciation, depletion and amortization ....      (12,486)   (11,530)
                                                            -------   --------
      Net property and equipment .....................       15,813     16,345
                                                            -------   --------

Total Assets .........................................      $26,013    $25,215
                                                            =======    =======

                       LIABILITIES AND PARTNERSHIP CAPITAL

Current liabilities:
    Accounts payable and other current liabilities ...      $   570    $   411
    Production and property taxes payable or accrued .          638        820
    Royalties and production payment payable .........          497      1,063
    Distributions payable to Unitholders .............        1,958      1,958
                                                            -------    -------
      Total current liabilities ......................        3,663      4,252
Long-term debt .......................................          100        122
                                                            -------    -------
      Total liabilities ..............................        3,763      4,374

Commitments and contingencies (Note 2)

Partnership capital
    General partners .................................          145        131
    Unitholders ......................................       22,105     20,710
                                                            -------    -------
      Total partnership capital ......................       22,250     20,841
                                                            -------    -------

Total liabilities and partnership capital ............      $26,013    $25,215
                                                            =======    =======

                     The accompanying condensed notes are an
                   integral part of hese financial statements.

<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)


                        CONDENSED STATEMENTS OF EARNINGS
                                   (Unaudited)

            For the Three and Six Months Ended June 30, 1998 and 1997
                            (In Thousands of Dollars)




                                       Three Months Ended      Six Months Ended
                                             June 30,              June 30,
                                       ------------------      ----------------
                                         1998       1997        1998     1997
                                       --------   -------      -------  -------

Net operating revenues:
     Natural gas sales ..............  $ 4,129    $ 3,840      $ 8,379  $ 9,863
     Other ..........................       55         42          104       92
     Production payment (ORRI) ......     (193)      (187)        (395)    (531)
                                       -------    -------     -------- --------
Total net operating revenues .......     3,991      3,695        8,088    9,424
                                       -------    -------     -------- --------
Costs and expenses
    Operating, including prod. taxes       940        849        1,818    1,833
    Depletion, depreciation & amort.       495        458        1,000      943
    General and administrative .....       131        134          274      282
    Management fees ................       124         97          249      213
    Interest .......................        10         20           20       78
    Other income, net ..............       (70)       (46)         (98)     (67)
                                       -------    -------     -------- --------
Total costs and expenses ...........     1,630      1,512        3,263    3,282
                                       -------    -------     --------  -------
Net earnings .......................   $ 2,361    $ 2,183     $  4,825  $ 6,142
                                       =======    =======     ========  =======
Net earnings per Unit (in dollars) .   $  0.22    $  0.21     $   0.45  $  0.57
                                       =======    =======     ========  =======





                     The accompanying condensed notes are an
                  integral part of these financial statements.


<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)


                       CONDENSED STATEMENTS OF CASH FLOWS
                                   (Unaudited)

                 For the Six Months Ended June 30, 1998 and 1997
                            (In Thousands of Dollars)




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

Cash flows provided by operating activities ..........     $ 5,384      $ 7,883
                                                           -------      -------
Cash flows used in investing activities:
    Purchases of prop. & equipment ...................        (475)        (746)
    Purchase of securities - available for sale ......        (741)         -0-
    Cash received on sale of other prop. & equipment..         -0-           34
                                                           -------      -------
Cash flows used in investing activities ..............      (1,216)        (712)
                                                           -------      -------
Cash flows used in financing activities:
    Distributions paid to Unitholders ................      (3,907)      (3,799)
    Additions to long-term debt ......................         -0-        5,200
    Reductions of long-term debt .....................         (22)      (8,222)
                                                           -------      -------
Cash flows used in financing activities ..............      (3,929)      (6,821)
                                                           -------      -------

Increase in cash and cash equivalents ................         239          350
Cash and cash equivalents at January 1, ..............       3,344          115
                                                           -------      -------
Cash and cash equivalents at June 30, ................     $ 3,583      $   465
                                                           =======      =======












                     The accompanying condensed notes are an
                  integral part of these financial statements.
<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)

                     NOTES TO CONDENSED FINANCIAL STATEMENTS
                                   (Unaudited)

1.   The condensed financial statements reflect all adjustments (consisting only
     of normal,  recurring adjustments and certain adjustments discussed in Note
     2)  which  are,  in  the  opinion  of  management,  necessary  for  a  fair
     presentation of Dorchester Hugoton, Ltd.'s (the "Partnership's")  financial
     position  and  operating  results for the interim  period.  Interim  period
     results are not  necessarily  indicative  of the  results for the  calendar
     year.  Please refer to  Management's  Discussion  and Analysis of Financial
     Condition and Results of Operations  for additional  information.  Per-Unit
     information is calculated by dividing the 99% interest owned by Unitholders
     by the 10,744,380 Units outstanding.

2.   Through December 31, 1997 the Partnership recorded $500,000 (which included
     related  interest)  towards  a request  from  Panhandle  Eastern  Pipe Line
     Company  ("PEPL") for refund of Kansas tax  reimbursements  received by the
     Partnership  during the years 1983 to 1987.  These charges  resulted from a
     ruling by the United  States  Court of Appeals for the District of Columbia
     which  overruled  a  previous  order  by  the  Federal  Energy   Regulatory
     Commission.  The Partnership and PEPL reached agreement on a portion of the
     disputed  amounts  and on March 9, 1998  $151,756.92  was paid to PEPL.  An
     additional    $366,633.13,     which    is    still    awaiting    possible
     regulatory/judicial/legislative  action, was placed into an escrow account.
     At June 30, the value of the escrow is approximately $370,000. The escrowed
     funds  include  amounts  possibly  waived,  recovered or  recoverable  from
     others. A reduction to operating  expense of $51,000 offset by an allowance
     of $36,000 for the uncollectible  portion not waived has been booked during
     the first six months of 1998.

3.   Since 1994 the  Partnership  has maintained an unsecured  revolving  credit
     facility for $15,000,000 (the  "Agreement")  with Bank One, Texas, N.A. The
     Agreement  has a  current  borrowing  base  of  $6,000,000,  which  will be
     re-evaluated by Bank One at least semi-annually.  If, on any such date, the
     aggregate  amount of  outstanding  loans and  letters of credit  exceed the
     current  borrowing  base, the  Partnership is required to repay the excess.
     This credit  facility  covers both cash  advances and any letters of credit
     that the Partnership may need, with interest being charged at the base rate
     for Bank One, which was 8.5% on July 31, 1998.  All amounts  borrowed under
     this  facility will become due and payable on July 31, 1999. As of July 31,
     1998,  letters of credit  totaling  $25,000  were  issued  under the credit
     facility and the amount borrowed was $100,000.  The weighted average amount
     borrowed  under the credit  facility  remained  $100,000  during the second
     quarter of 1998.

4.   Comprehensive  income,  as defined in  Statement  of  Financial  Accounting
     Standards No. 130, includes holding gains on investments available for sale
     and is calculated below:
                                        Three Months Ended    Six Months Ended
                                        ------------------    -----------------
                                             June 30,             June 30,
                                        ------------------    -----------------
                                         1998        1997      1998       1997
                                        ------      ------    ------     ------
      Net earnings....................  $2,361      $2,183    $4,825     $6,142
      Unrealized holding gain on
        available for sale securities.     175         398       523        661
                                        ------      ------    ------     ------
      Comprehensive income............  $2,536      $2,581    $5,348     $6,803
                                        ======      ======    ======     ======
<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)
PART I
Item 2
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


Net cash flows from operating  activities  during the three and six months ended
June 30,  1998  were  $2,497,000  and  $5,384,000  compared  to  $3,157,000  and
$7,883,000  for the same  periods of 1997.  Second  quarter 1998 cash flows from
operating activities were impacted by modest increases in second quarter natural
gas market prices and by slightly  lower  natural gas sales volumes  compared to
the  second  quarter of 1997.  Second  quarter  1997 cash flows were  positively
impacted by the timing of receivable  collections at month-end compared to 1998.
Since the second quarter of 1997, the Partnership has shortened the time between
sales of gas production and receipt of payment.  Six month  operating cash flows
have been negatively impacted during 1998 by lower natural gas market prices and
lower 1998 gas sales volumes compared to the same period of 1997.  During March,
1998 the Partnership also paid to Panhandle Eastern Pipe Line Company or into an
escrow account approximately $500,000 (See Note 2 to the Financial Statements).

The Partnership has available a $15,000,000  unsecured revolving credit facility
with a current borrowing base of $6,000,000.  Please see Note 3 to the financial
statements for additional  information.  As of July 31, 1998,  letters of credit
totaling  $25,000 were issued under the credit  facility and the amount borrowed
was $100,000. The weighted average amount borrowed under the credit facility was
$100,000 during the first and second quarter of 1998. Cash and cash  equivalents
totaled $3,583,000 at June 30, 1998 compared to $3,344,000 on December 31, 1997.
During the quarter  ending June 30, 1998, the  Partnership  increased its common
stock holdings in Exxon Corp. by 10,000 shares to 64,000 shares.

In connection with the Oklahoma properties, on May 15, 1998 the Partnership paid
approximately  $847,000 in production  payments for the year ended  February 28,
1998; an additional  $241,000 has been accrued through June 30, 1998. During the
quarter  ending June 30, 1998,  the  Partnership  completed a  transaction  that
resulted  in  the  sale  of  the  Partnership's  50%  working  interest  in  one
non-operated  Oklahoma  well and the  Partnership's  acquisition  of  overriding
royalty  interests in one Partnership  owned and operated Oklahoma well. The net
cash outlay by the Partnership in the transaction  was  approximately  $166,000.
During July,  1998 the Partnership  acquired for $220,000 a royalty  interest in
Kansas of  approximately  3% that included two wells operated by the Partnership
and two non-Hugoton wells operated by others .

The  Partnership's  portion  of gas sales  volumes  (not  reduced  for  Oklahoma
production payment) and weighted average sales prices were:

                                  Three Months Ended           Six Months Ended
                               ----------------------------    -----------------
                                   June 30,                         June 30,
                               ----------------     Mar. 31,   -----------------
                                1998       1997       1998      1998       1997
Sales Volumes - MMCF:          -----      -----      -----     -----      -----
   Oklahoma ...............    1,410      1,387      1,439     2,849      2,878
   Kansas .................      435        491        466       901        991
                               -----      -----      -----     -----      -----
Total MMCF ................    1,845      1,878      1,905     3,750      3,869
                               =====      =====      =====     =====      =====
Weighted Average Sales Prices - $/MCF:
   Oklahoma ...............    $2.22      $2.04      $2.21     $2.21      $2.55
   Kansas .................     2.30       2.06       2.30      2.30       2.55
Overall Weighted Avg - $/MCF   $2.24      $2.04      $2.23      2.23       2.55
<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)

PART I
Item 2
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS
                                   (Continued)



Oklahoma gas sales  volumes were  essentially  unchanged  during the 1998 second
quarter  compared to the  previous  1998 quarter and compared to the 1997 second
quarter as well as for the comparable six month periods of 1997 and 1998. Kansas
1998 gas sales  volumes  during the second  quarter were  slightly less than the
first  quarter of 1998.  Compared to 1997,  Kansas 1998 gas sales  volumes  were
lower  than the  comparable  1997  second  quarter  and the 1997  same six month
period.  Such  decreases  are primarily a result of natural  reservoir  declines
experienced by the Partnership and other producers in the Kansas area.

As previously  announced in the Partnership's March 31, 1998 Quarterly Report on
Form 10-Q,  the  Partnership  drilled and  completed its second well to test the
Guymon-Hugoton  field Fort  Riley zone in  Oklahoma.  The second  well's  recent
production  of 125 MCF per day while  pumping 50 bbls of water per day is not as
favorable as the now plugged  original well on the same acreage  which  produced
approximately  175  MCF per day  with no  water  from  the  upper  zones  of the
Guymon-Hugoton field. Present state regulations do not allow gas production from
two Guymon-Hugoton  field wells on the same 640 acres.  However,  the Fort Riley
production from the lower zone is all NEW production.  The previously  producing
upper  zone  reserves  can later be  produced  from this same  second  well upon
ceasing  production  from the Fort Riley zone.  As  discussed in the 1997 Annual
Report on Form 10-K, the  Partnership's  1997 Matter 2A well, which now produces
about 426 MCF per day,  was  inconclusive  as to Fort  Riley  productivity.  The
Partnership  anticipates  attempting another Fort Riley well during the next few
months.  IT IS NOT KNOWN HOW MANY WELLS  SHOULD BE  ATTEMPTED  TO  EVALUATE  THE
POTENTIAL  OF THE FORT  RILEY  FORMATION.  THE  OUTCOME OF SUCH  EXPLORATION  IS
UNPREDICTABLE.

In 1997 and prior  Annual  Reports  on Form  10-K,  the  Partnership's  property
interests  have  been  described  as  relatively   shallow   Guymon-Hugoton   or
Kansas-Hugoton  without  specific  details  regarding  depth.  Because  of newly
announced  plans by others  for deeper  drilling  underlying  the  Partnership's
acreage,  the  Partnership  clarifies  that it owns the Council Grove  formation
under most of the Partnership's acreage in Oklahoma. The Partnership owns only a
minor  overriding  royalty  interest  in the  Kansas  Council  Grove  formation.
Production from the relatively shallow Oklahoma Council Grove (which is not part
of the  Guymon-Hugoton  field) is presently  non-existent  on the  Partnership's
acreage;  however,  two wells on  adjoining  acreage  have been  completed.  The
Partnership has begun looking into such offsetting activity.  IT IS NOT KNOWN IF
SUCH CLOSER LOOK WILL RESULT IN ANY PLANS BY THE PARTNERSHIP TO ATTEMPT DRILLING
A COUNCIL  GROVE WELL.  All previous  preliminary  reviews  yielded  unfavorable
predictions.


<PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)

PART I
Item 2
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS
                                   (Continued)




As previously  discussed in the  Partnership's  1997 Annual Report on Form 10-K,
the routine workover of wells in Kansas and Oklahoma  included fracture treating
(the creation of cracks in the formation to assist gas flow toward the well bore
from the producing  zones).  While the results of one workover in Kansas was not
successful in improving production or increasing  pressure,  five well workovers
in Oklahoma are all  producing  increased  volumes.  Four of the five wells have
increased in pressure which combined with increased  additional volume generally
indicates  increased  reserves.  Such fracture  treatments  cost from $25,000 to
$75,000 per well. HOWEVER, THE RESULTS OF SUCH FRACTURE TREATING CAN VARY WIDELY
FROM  WELL  TO  WELL  AND MAY NOT BE  SUCCESSFUL.  The  Partnership  anticipates
continuing additional fracture treating during 1998.

As  previously  discussed in the 1997 Annual Report on Form 10-K, on February 4,
1998 the Oklahoma  Corporation  Commission ("OCC"),  which administers state oil
and gas conservation,  adopted rules that will essentially  remove limits on all
gas well  production  volume in the Guymon Hugoton field including most gas from
the  Partnership's  wells. The effective date and actual  publication of the new
rules are still  pending.  The OCC  specifically  provided that the rule changes
have no  bearing  on the  question  of infill  drilling  which  must be  decided
separately.  Infill drilling,  if adopted,  would likely allow one well for each
320 acres (as in the  Partnership's  Kansas  properties)  versus the present one
well for each 640 acres. Both infill drilling and elimination of the field rules
could require  considerable capital  expenditures.  THE OUTCOME AND COST OF SUCH
ACTIVITIES IS UNPREDICTABLE.

The   Partnership   is  in  the  process  of  reviewing  and  making   necessary
modifications to its computer  systems for year 2000 compliance.  Costs incurred
to date to modify the Partnership's computer systems have not been material, and
future  costs  are  not  expected  to be  material.  Timely  completion  of such
modifications  is not  considered  to be a  material  risk to the  Company.  The
Partnership  is in the  process of  initiating  formal  communications  with its
significant  suppliers and large  customers to determine the extent to which the
Partnership's  operations may be potentially  vulnerable to those third parties'
failure to prepare for the year 2000 change.

As previously  discussed in the 1997 Annual Report on Form 10-K, the Partnership
is reviewing  its  strategic  alternatives  in light of the various  mergers and
other business  transactions  occurring in the natural gas and energy  industry.
Although no decision to sell or combine the  Partnership's  business with others
has been made,  the  Partnership  anticipates  possible  discussions  with third
parties which could result in such a decision.  The Partnership has no timetable
for any such  discussions,  and there is no assurance that any such  discussions
will lead to a  transaction.  During the first  quarter of 1998 the  Partnership
adopted a severance policy which would provide up to approximately  $2.8 million
of severance  payments if such obligations  occur. While the Partnership has not
repurchased and retired any of its publicly traded Units to date, the previously
announced program is still in place.
 <PAGE>
                            DORCHESTER HUGOTON, LTD.
                          (A Texas Limited Partnership)

                                OTHER INFORMATION
PART II

     Item 1. Legal  Proceedings:  See Notes to Condensed  Financial  Statements.

     Item 5. Other Information:  Effective September 8, 1998, the transfer agent
             for the  Partnership's depositary  units will change from  American
             Stock  Transfer  &  Trust  Company  to  BankBoston,  N.A.,  %Boston
             EquiServe Limited Partnership, 150 Royall Street, Canton, MA 02021.

     Item 6. Exhibits  and  Reports  on Form 8-K:
         a)  Exhibit  27 -  Financial  Data Schedule
         b)  Reports on Form 8-K - None.



                                   SIGNATURES

Pursuant  to the  requirements  of the  Securities  Exchange  Act of  1934,  the
Registrant  has duly  caused  this  report  to be  signed  on its  behalf by the
undersigned thereunto duly authorized.


                                       DORCHESTER HUGOTON, LTD.
                                       Registrant





Date:July 31, 1998                     /s/ Kathleen A. Rawlings
                                       Kathleen A. Rawlings
                                       Controller (Principal Accounting Officer)