SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549



                                  FORM 10-Q


               Quarterly Report Pursuant to Section 13 or 15(d)
                    of the Securities Exchange Act of 1934


For the quarter ended                     Commission File Number
  September 30, 1998                                    0-10442



                       DYCO OIL AND GAS PROGRAM 1981-1
                           (A LIMITED PARTNERSHIP)
            (Exact Name of Registrant as specified in its charter)



         Minnesota                         41-1411953
(State or other jurisdiction    (I.R.S. Employer Identification
   of incorporation or                       Number)
     organization)



Samson Plaza, Two West Second Street, Tulsa, Oklahoma  74103
------------------------------------------------------------
(Address of principal executive offices)          (Zip Code)



                              (918) 583-1791
       ----------------------------------------------------
        (Registrant's telephone number, including area code)


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
                            ------                    ------




                                       1
<PAGE>




                        PART I. FINANCIAL INFORMATION


ITEM 1.  FINANCIAL STATEMENTS

             DYCO OIL AND GAS PROGRAM 1981-1 LIMITED PARTNERSHIP
                                BALANCE SHEETS
                                 (Unaudited)

                                    ASSETS

                                             September 30,     December 31,
                                                  1998            1997
                                               ----------      ------------

CURRENT ASSETS:
   Cash and cash equivalents                     $19,397          $118,975
   Accrued oil and gas sales                      24,674            27,837
                                                 -------          --------
      Total current assets                       $44,071          $146,812

NET OIL AND GAS PROPERTIES, utilizing
   the full cost method                           41,855            71,444

DEFERRED CHARGE                                    3,334             3,334
                                                 -------          --------
                                                 $89,260          $221,590
                                                 =======          ========

                 LIABILITIES AND PARTNERS' CAPITAL (DEFICIT)

CURRENT LIABILITIES:
   Accounts payable                              $ 2,839          $  3,225
   Gas imbalance payable                           2,249            47,188
                                                 -------          --------
      Total current liabilities                  $ 5,088          $ 50,413

ACCRUED LIABILITY                                $85,405          $ 85,405

PARTNERS' CAPITAL (DEFICIT):
   General Partner, issued and
      outstanding, 70 units                     ($    13)         $    857
   Limited Partners, issued and
      outstanding, 7,000 units                  (  1,220)           84,915
                                                 -------          --------
      Total Partners' capital (deficit)         ($ 1,233)         $ 85,772
                                                 -------          --------
                                                 $89,260          $221,590
                                                 =======          ========


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



                                       2
<PAGE>



             DYCO OIL AND GAS PROGRAM 1981-1 LIMITED PARTNERSHIP
                           STATEMENTS OF OPERATIONS
            FOR THE THREE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997
                                 (Unaudited)

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

REVENUES:
   Oil and gas sales                             $53,237           $29,425
   Interest                                        1,568             1,058
                                                 -------           -------
                                                 $54,805           $30,483

COSTS AND EXPENSES:
   Oil and gas production                        $ 7,120           $ 9,749
   Depreciation, depletion, and
      amortization of oil and gas
      properties                                  11,009             2,430
   General and administrative
      (Note 2)                                    14,793            16,248
                                                 -------           -------
                                                 $32,922           $28,427
                                                 -------           -------

NET INCOME                                       $21,883           $ 2,056
                                                 =======           =======
GENERAL PARTNER (1%) - net
   income                                        $   219           $    21
                                                 =======           =======
LIMITED PARTNERS (99%) - net
   income                                        $21,664           $ 2,035
                                                 =======           =======
NET INCOME PER UNIT                              $  3.09           $   .29
                                                 =======           =======
UNITS OUTSTANDING                                  7,070             7,070
                                                 =======           =======



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



                                       3
<PAGE>



             DYCO OIL AND GAS PROGRAM 1981-1 LIMITED PARTNERSHIP
                           STATEMENTS OF OPERATIONS
            FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997
                                 (Unaudited)

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

REVENUES:
   Oil and gas sales                            $159,317          $146,949
   Interest                                        4,197             3,500
                                                --------          --------
                                                $163,514          $150,449

COSTS AND EXPENSES:
   Oil and gas production                       $ 28,471          $ 54,400
   Depreciation, depletion, and
      amortization of oil and gas
      properties                                  26,135            16,717
   General and administrative
      (Note 2)                                    54,513            60,451
                                                --------          --------
                                                $109,119          $131,568
                                                --------          --------

NET INCOME                                      $ 54,395          $ 18,881
                                                ========          ========
GENERAL PARTNER (1%) - net
   income                                       $    544          $    189
                                                ========          ========
LIMITED PARTNERS (99%) - net
   income                                       $ 53,851          $ 18,692
                                                ========          ========
NET INCOME PER UNIT                             $   7.69          $   2.67
                                                ========          ========
UNITS OUTSTANDING                                  7,070             7,070
                                                ========          ========



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



                                       4
<PAGE>



             DYCO OIL AND GAS PROGRAM 1981-1 LIMITED PARTNERSHIP
                           STATEMENTS OF CASH FLOWS
            FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997
                                 (Unaudited)


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

CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                   $ 54,395          $ 18,881
   Adjustments to reconcile net income
      to net cash provided by operating
      activities:
      Depreciation, depletion, and
        amortization of oil and gas
        properties                                26,135            16,717
      Decrease in accrued oil and
        gas sales                                  3,163            32,622
      Decrease in accounts payable             (     386)        (   7,707)
      Decrease in gas imbalance payable        (  44,939)                -
                                                --------          --------
      Net cash provided by operating
        activities                              $ 38,368          $ 60,513
                                                --------          --------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Proceeds from the sale of oil and
      gas properties                            $  3,839          $ 26,506
   Additions to oil and gas
      properties                               (     385)        (   1,501)
                                                --------          --------
   Net cash provided by investing
      activities                                $  3,454          $ 25,005
                                                --------          --------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Cash distributions                          ($141,400)        ($176,750)
                                                --------          --------
   Net cash used by financing
      activities                               ($141,400)        ($176,750)
                                                --------          --------

NET DECREASE IN CASH AND CASH
   EQUIVALENTS                                 ($ 99,578)        ($ 91,232)

CASH AND CASH EQUIVALENTS AT
   BEGINNING OF PERIOD                           118,975           197,842
                                                --------          --------
CASH AND CASH EQUIVALENTS AT
   END OF PERIOD                                $ 19,397          $106,610
                                                ========          ========


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


                                       5
<PAGE>



             DYCO OIL AND GAS PROGRAM 1981-1 LIMITED PARTNERSHIP
                   CONDENSED NOTES TO FINANCIAL STATEMENTS
                              SEPTEMBER 30, 1998
                                  (Unaudited)


1.     ACCOUNTING POLICIES
      -------------------

      The balance sheet as of September 30, 1998,  statements of operations  for
      the  three  and  nine  months  ended  September  30,  1998 and  1997,  and
      statements of cash flows for the nine months ended  September 30, 1998 and
      1997  have been  prepared  by Dyco  Petroleum  Corporation  ("Dyco"),  the
      General Partner of the Dyco Oil and Gas Program 1981-1 Limited Partnership
      (the  "Program"),   without  audit.  In  the  opinion  of  management  all
      adjustments (which include only normal recurring adjustments) necessary to
      present  fairly the financial  position at September 30, 1998,  results of
      operations  for the three and nine  months  ended  September  30, 1998 and
      1997,  and changes in cash flows for the nine months ended  September  30,
      1998 and 1997 have been made.

      Information  and  footnote  disclosures  normally  included  in  financial
      statements  prepared in  accordance  with  generally  accepted  accounting
      principles  have been  condensed or omitted.  It is  suggested  that these
      financial  statements be read in conjunction with the financial statements
      and notes thereto included in the Program's Annual Report on Form 10-K for
      the year ended December 31, 1997. The results of operations for the period
      ended September 30, 1998 are not necessarily  indicative of the results to
      be expected for the full year.


      OIL AND GAS PROPERTIES
      ----------------------

      Oil and gas  operations  are  accounted  for using the full cost method of
      accounting.  All productive and  non-productive  costs associated with the
      acquisition,  exploration  and  development  of oil and gas  reserves  are
      capitalized.  The Program's  calculation of depreciation,  depletion,  and
      amortization  includes  estimated  future  expenditures  to be incurred in
      developing  proved  reserves and estimated  dismantlement  and abandonment
      costs, net of estimated  salvage values. In the event the unamortized cost
      of oil and gas properties  being  amortized  exceeds the full cost ceiling
      (as defined by the  Securities  and  Exchange  Commission),  the excess is
      charged to expense in the period  during which such excess  occurs.  Sales
      and abandonments of





                                       6
<PAGE>



      properties are accounted for as  adjustments of capitalized  costs with no
      gain or loss recognized, unless such adjustments would significantly alter
      the  relationship  between  capitalized  costs  and  proved  oil  and  gas
      reserves.

      The provision for depreciation, depletion, and amortization of oil and gas
      properties is calculated by dividing the oil and gas sales dollars  during
      the  period by the  estimated  future  gross  income  from the oil and gas
      properties and applying the resulting  rate to the net remaining  costs of
      oil and gas properties that have been  capitalized,  plus estimated future
      development costs.


2.     TRANSACTIONS WITH RELATED PARTIES
      ---------------------------------

      Under the terms of the Program's partnership  agreement,  Dyco is entitled
      to  receive a  reimbursement  for all  direct  expenses  and  general  and
      administrative, geological and engineering expenses it incurs on behalf of
      the Program. During the three months ended September 30, 1998 and 1997 the
      Program incurred such expenses totaling $14,793 and $16,248, respectively,
      of which $12,513 was paid each period to Dyco and its  affiliates.  During
      the nine months  ended  September  30, 1998 and 1997 the Program  incurred
      such expenses totaling $54,513 and $60,451, respectively, of which $37,539
      was paid each period to Dyco and its affiliates.

      Affiliates of the Program  operate  certain of the  Program's  properties.
      Their  policy is to bill the  Program for all  customary  charges and cost
      reimbursements associated with these activities.





                                       7
<PAGE>



ITEM 2.     MANAGEMENT'S  DISCUSSION  AND ANALYSIS OF FINANCIAL  CONDITION AND
            RESULTS OF OPERATIONS


USE OF FORWARD-LOOKING STATEMENTS AND ESTIMATES
-----------------------------------------------

      This Quarterly Report contains  certain  forward-looking  statements.  The
      words "anticipate",  "believe",  "expect",  "plan", "intend",  "estimate",
      "project", "could", "may" and similar expressions are intended to identify
      forward-looking  statements.  Such statements reflect management's current
      views  with  respect  to future  events and  financial  performance.  This
      Quarterly Report also includes certain information,  which is, or is based
      upon,  estimates  and  assumptions.  Such  estimates and  assumptions  are
      management's  efforts to accurately reflect the condition and operation of
      the Program.

      Use of  forward-looking  statements and estimates and assumptions  involve
      risks  and  uncertainties  which  include,  but are not  limited  to,  the
      volatility of oil and gas prices, the uncertainty of reserve  information,
      the operating risk associated  with oil and gas properties  (including the
      risk of personal injury,  death,  property  damage,  damage to the well or
      producing  reservoir,  environmental  contamination,  and other  operating
      risks), the prospect of changing tax and regulatory laws, the availability
      and capacity of  processing  and  transportation  facilities,  the general
      economic climate,  the supply and price of foreign imports of oil and gas,
      the level of consumer  product demand,  and the price and  availability of
      alternative  fuels.  Should  one or more of these  risks or  uncertainties
      occur or should  estimates  or  underlying  assumptions  prove  incorrect,
      actual  conditions or results may vary materially and adversely from those
      stated, anticipated, believed, estimated, and otherwise indicated.


LIQUIDITY AND CAPITAL RESOURCES
-------------------------------

      Net  proceeds  from the  Program's  operations  less  necessary  operating
      capital  are  distributed  to  investors  on a  quarterly  basis.  The net
      proceeds from production are not reinvested in productive  assets,  except
      to the extent  that  producing  wells are  improved  or where  methods are
      employed to permit more efficient recovery of the Program's reserves which
      would result in a positive economic impact.





                                       8
<PAGE>



      The Program's  available capital from  subscriptions has been spent on oil
      and gas  drilling  activities.  There  should not be any further  material
      capital  resource  commitments  in the  future.  The  Program  has no debt
      commitments. Cash for operational purposes will be provided by current oil
      and gas production.


RESULTS OF OPERATIONS
---------------------

      GENERAL DISCUSSION

      The following  general  discussion  should be read in conjunction with the
      analysis  of results of  operations  provided  below.  The most  important
      variable  affecting the Program's  revenues is the prices received for the
      sale  of  oil  and  gas.  Predicting  future  prices  is  very  difficult.
      Substantially  all of the  Program's  gas  reserves  are being sold on the
      "spot market".  Prices on the spot market are subject to wide seasonal and
      regional pricing  fluctuations due to the highly competitive nature of the
      spot market. Such spot market sales are generally short-term in nature and
      are dependent upon the obtaining of  transportation  services  provided by
      pipelines. In addition, crude oil prices are at or near their lowest level
      in the past  decade  due  primarily  to the  global  surplus of crude oil.
      Management is unable to predict whether future oil and gas prices will (i)
      stabilize, (ii) increase, or (iii) decrease.

      THREE  MONTHS  ENDED  SEPTEMBER  30, 1998 AS COMPARED TO THE THREE  MONTHS
      ENDED SEPTEMBER 30, 1997.

                                              Three Months Ended September 30,
                                              --------------------------------
                                                   1998              1997
                                                  -------           -------
      Oil and gas sales                           $53,237           $29,425
      Oil and gas production expenses             $ 7,120           $ 9,749
      Barrels produced                                  4                55
      Mcf produced                                 27,866            19,082
      Average price/Bbl                           $ 13.50           $ 19.31
      Average price/Mcf                           $  1.91           $  1.49

      As shown in the table  above,  total oil and gas sales  increased  $23,812
      (80.9%) for the three months ended  September  30, 1998 as compared to the
      three months ended  September  30, 1997. Of this  increase,  approximately
      $13,000  was  related  to an  increase  in the  volumes  of gas  sold  and
      approximately  $12,000 was related to an increase in the average  price of
      gas sold.  Volumes of oil sold decreased 51 barrels,  while volumes of gas
      sold increased 8,784 Mcf, for the three months ended September 30, 1998 as
      compared to the three months ended September 30, 1997. The increase in



                                       9
<PAGE>



      volumes  of gas sold  resulted  primarily  from the  curtailment  of sales
      during the three months ended September 30, 1997 on one  significant  well
      due to the  Program's  overproduced  position  in that well.  Average  oil
      prices decreased to $13.50 per barrel for the three months ended September
      30, 1998 from $19.31 per barrel for the three months ended  September  30,
      1997.  Average gas prices  increased to $1.91 per Mcf for the three months
      ended  September  30, 1998 from $1.49 per Mcf for the three  months  ended
      September 30, 1997.

      Oil and gas production  expenses  (including lease operating  expenses and
      production  taxes)  decreased  $2,629  (27.0%) for the three  months ended
      September  30, 1998 as compared to the three  months ended  September  30,
      1997. This decrease resulted  primarily from a negative prior period lease
      operating expense  adjustment by the operator on one well during the three
      months ended  September  30, 1998.  As a percentage  of oil and gas sales,
      these expenses decreased to 13.4% for the three months ended September 30,
      1998 from  33.1% for the three  months  ended  September  30,  1997.  This
      percentage decrease was primarily due to the dollar decrease in production
      expenses and the  increase in the average  price of gas sold for the three
      months  ended  September  30, 1998 as compared to the three  months  ended
      September 30, 1997.

      Depreciation,  depletion,  and  amortization  of oil  and  gas  properties
      increased $8,579 (353.0%) for the three months ended September 30, 1998 as
      compared to the three  months ended  September  30,  1997.  This  increase
      resulted primarily from (i) the increase in volumes of gas sold during the
      three  months  ended  September  30, 1998 as compared to the three  months
      ended  September  30,  1997 and (ii) a decrease  in the oil and gas prices
      used in the  valuation  of reserves at  September  30, 1998 as compared to
      September  30, 1997.  As a percentage  of oil and gas sales,  this expense
      increased to 20.7% for the three months ended September 30, 1998 from 8.3%
      for the three months ended September 30, 1997.  This  percentage  increase
      was  primarily  due to the  decrease in the oil and gas prices used in the
      valuation of reserves at September  30, 1998 as compared to September  30,
      1997.

      General and administrative  expenses decreased $1,455 (9.0%) for the three
      months  ended  September  30, 1998 as compared to the three  months  ended
      September 30, 1997. As a percentage of oil and gas sales,  these  expenses
      decreased  to 27.8% for the three  months  ended  September  30, 1998 from
      55.2% for the three  months ended  September  30,  1997.  This  percentage
      decrease was primarily due to the increase in oil and gas sales.





                                       10
<PAGE>



     NINE MONTHS ENDED  SEPTEMBER  30, 1998 AS COMPARED TO THE NINE MONTHS ENDED
     SEPTEMBER 30, 1997.

                                              Nine Months Ended September 30,
                                              -------------------------------
                                                   1998              1997
                                                 --------          --------
      Oil and gas sales                          $159,317          $146,949
      Oil and gas production expenses            $ 28,471          $ 54,400
      Barrels produced                                134               158
      Mcf produced                                 79,633            67,281
      Average price/Bbl                          $  14.56          $  19.81
      Average price/Mcf                          $   1.98          $   2.14

      As shown in the table  above,  total oil and gas sales  increased  $12,368
      (8.4%) for the nine  months  ended  September  30, 1998 as compared to the
      nine months ended  September  30, 1997.  Of this  increase,  approximately
      $26,000 was  related to an increase in the volumes of gas sold,  which was
      partially offset by a decrease of approximately  $13,000 due to a decrease
      in the average price of gas sold. Volumes of oil sold decreased 24 barrels
      while volumes of gas sold  increased  12,352 Mcf for the nine months ended
      September  30, 1998 as compared to the nine  months  ended  September  30,
      1997.  The  increase in volumes of gas sold  resulted  primarily  from the
      curtailment  of sales during the nine months ended  September  30, 1997 on
      one significant  well due to the Program's  overproduced  position in that
      well.  Average oil and gas prices decreased to $14.56 per barrel and $1.98
      per Mcf,  respectively,  for the nine months ended September 30, 1998 from
      $19.81  per barrel and $2.14 per Mcf,  respectively,  for the nine  months
      ended September 30, 1997.

      Oil and gas production  expenses  (including lease operating  expenses and
      production  taxes)  decreased  $25,929  (47.7%) for the nine months  ended
      September  30, 1998 as compared to the nine  months  ended  September  30,
      1997. This decrease resulted primarily from (i) workover expenses incurred
      on one well during the nine months  ended  September  30, 1997 in order to
      improve  the  recovery  of  reserves  and (ii) the sale of one well during
      1997. As a percentage of oil and gas sales,  these  expenses  decreased to
      17.9% for the nine months ended September 30, 1998 from 37.0% for the nine
      months ended September 30, 1997.  This  percentage  decrease was primarily
      due to the dollar decrease in oil and gas production expenses.




                                       11
<PAGE>



      Depreciation,  depletion,  and  amortization  of oil  and  gas  properties
      increased  $9,418 (56.3%) for the nine months ended  September 30, 1998 as
      compared  to the nine months  ended  September  30,  1997.  This  increase
      resulted primarily from (i) the increase in volumes of gas sold during the
      nine months ended  September 30, 1998 as compared to the nine months ended
      September 30, 1997 and (ii) a decrease in the prices used in the valuation
      of oil and gas reserves at September 30, 1998 as compared to September 30,
      1997.  As a percentage  of oil and gas sales,  this  expense  increased to
      16.4% for the nine months ended September 30, 1998 from 11.4% for the nine
      months ended September 30, 1997.  This  percentage  increase was primarily
      due to the  decrease  in the oil and gas prices used in the  valuation  of
      reserves at September 30, 1998 as compared to September 30, 1997.

      General and  administrative  expenses decreased $5,938 (9.8%) for the nine
      months  ended  September  30, 1998 as  compared  to the nine months  ended
      September 30, 1997. As a percentage of oil and gas sales,  these  expenses
      decreased to 34.2% for the nine months ended September 30, 1998 from 41.1%
      for the nine months ended September 30, 1997. This percentage decrease was
      primarily  due  to the  dollar  decrease  in  general  and  administrative
      expenses and the increase in oil and gas sales.




                                       12
<PAGE>



                          PART II. OTHER INFORMATION

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

      (a)    Exhibits

               27.1     Financial  Data Schedule  containing  summary  financial
                        information  extracted from the Dyco Oil and Gas Program
                        1981-1 Limited Partnership's  financial statements as of
                        September  30,  1998  and  for  the  nine  months  ended
                        September 30, 1998, filed herewith.

                        All other exhibits are omitted as inapplicable.

      (b) Reports on Form 8-K.

            None.





                                       13
<PAGE>



                                  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.


                              DYCO OIL AND GAS PROGRAM 1981-1 LIMITED
                              PARTNERSHIP

                                    (Registrant)

                                    BY:   DYCO PETROLEUM CORPORATION

                                          General Partner


Date:  October 30, 1998             By:         /s/Dennis R. Neill
                                       -------------------------------
                                              (Signature)
                                              Dennis R. Neill
                                              President


Date:  October 30, 1998             By:         /s/Patrick M. Hall
                                       -------------------------------
                                              (Signature)
                                              Patrick M. Hall
                                              Chief Financial Officer



                                       14
<PAGE>



                              INDEX TO EXHIBITS


NUMBER      DESCRIPTION
------      -----------

 27.1       Financial Data Schedule  containing  summary  financial  information
            extracted   from  the  Dyco  Oil  and  Gas  Program  1981-1  Limited
            Partnership's  financial statements as of September 30, 1998 and for
            the nine
            months ended September 30, 1998, filed herewith.

            All other exhibits are omitted as inapplicable.