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 Quarter Ending September 30, 1998 Commission File #0-5704



                                 MAYNARD OIL COMPANY
               (Exact name of registrant as specified in its charter)




            Delaware                                  75-1362284
    (State or other jurisdic-                       (IRS Employer
     tion of incorporation)                       Identification No.)



             8080 N. Central Expressway, Suite 660, Dallas, Texas 75206


     Registrant's telephone number, including area code:    (214) 891-8880


          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, and  (2) has  been
     subject to such filing requirements for the past 90 days.

                                 Yes   X    No      


     Indicate the number of  shares outstanding of each of the issuer's classes
     of common stock, as of November 6, 1998.


                  4,886,168 shares of common stock, par value $0.10



                        MAYNARD OIL COMPANY AND SUBSIDIARIES

              Index to Consolidated Financial Statements and Schedules


                                                                 Page

     Part I.   Financial Information

          Consolidated Balance Sheets
               September 30, 1998 and December 31, 1997

          Consolidated Statements of Operations
               Nine Months and Three Months ended
               September 30, 1998 and 1997

          Consolidated Statements of Shareholders' Equity
               Nine Months ended September 30, 1998

          Consolidated Statements of Cash Flows
               Nine Months ended September 30, 1998 and 1997

          Notes to Consolidated Financial Statements

          Management's Discussion and Analysis of Financial
               Condition and Results of Operations

     Part II.  Other Information

          Item 6.   Exhibits and Reports on Form 8-K

     Signatures

     <TABLE>
                        MAYNARD OIL COMPANY AND SUBSIDIARIES
                             Consolidated Balance Sheets
     <CAPTION>
                                                 September 30    December 31,
                                                     1998            1997
                                                 (Unaudited)      (Audited) 
     <S>                                              <C>               <C>
     ASSETS
     Current assets:
        Cash and cash equivalents               $ 23,849,003    $ 24,584,288 
        Accounts receivable, trade                 3,121,210       3,267,255 
        Other current assets                         611,986         546,238 
            Total current assets                  27,582,199      28,397,781 

     Property and equipment, at cost:
        Oil and gas properties, successful
          efforts method                         105,197,747     104,031,352 
        Other property and equipment                 547,789         548,668 
                                                 105,745,536     104,580,020 
        Less accumulated depreciation and
         amortization                            (59,878,121)    (54,692,225)
             Net property and equipment           45,867,415      49,887,795 

                                                $ 73,449,614    $ 78,285,576 
     LIABILITIES AND SHAREHOLDERS' EQUITY
     Current liabilities:
        Current installments of long-term debt  $  5,000,000    $  5,000,000 
        Accounts payable                           2,533,216       4,271,662 
        Accrued expenses                           1,785,742       1,402,021 
        Income taxes payable                          40,799         220,798 
            Total current liabilities              9,359,757      10,894,481 

     Deferred income taxes                         2,832,000       2,632,000 
     Long-term debt                                7,500,000      11,250,000 

     Shareholders' equity:
        Preferred stock of $.50 par value.
          Authorized 1,000,000 shares; none
           issued                                        --              --  
        Common stock of $.10 par value.
          Authorized 20,000,000 shares;
          4,886,772 and 4,889,450 shares
           issued and outstanding                    488,677         488,945 
        Additional paid-in capital                18,831,138      18,831,138 
        Retained earnings                         34,438,042      34,189,012 
            Total shareholders' equity            53,757,857      53,509,095 

     Commitments                                $ 73,449,614    $ 78,285,576 

     See accompanying Notes to Consolidated Financial Statements.
     </TABLE>

     <TABLE>
                               MAYNARD OIL COMPANY AND SUBSIDIARIES


                                                     Consolidated Statements of Operations
         <CAPTION>
                                                            Nine Months ended                     Three Months ended
                                                              September 30,                          September 30,

                                                          1998             1997                1998             1997
         <S>                                          <C>               <C>                <C>              <C>
         Revenues:
            Oil and gas sales                         $12,694,374      $19,971,221         $ 3,871,029      $ 5,994,485 
            Interest and other                          1,038,331          892,693             361,019          305,769 
            Gain (loss) on disposition
              of assets                                     6,390          204,524              (3,405)         147,232 
                                                       13,739,095       21,068,438           4,228,643        6,447,486 
         Costs and expenses:
            Operating expenses                          6,462,956        7,530,286           2,031,659        2,578,098 
            Exploration, dry holes and
               abandonments  56,554                       447,821           11,244              57,061 
            General and administrative                    700,135          824,936             161,452          163,530 
            Depreciation and amortization               5,391,277        5,268,165           1,775,015        1,775,900 
            Interest and other                            766,498        1,008,656             230,800          324,533 
                                                       13,377,420       15,079,864            4,210,170       4,899,122 

              Income before income taxes                  361,675        5,988,574              18,473        1,548,364 

         Income tax expense (benefit)                      85,000        1,587,500             (30,000)         117,500 

              Net income                              $   276,675      $ 4,401,074         $    48,473       $1,430,864 

         Weighted average number of common
            shares outstanding                          4,888,652        4,889,450           4,887,274        4,889,450 

         Net income per common share                        $ .06            $ .90               $ .01            $ .29  


         See accompanying Notes to Consolidated Financial Statements.
         </TABLE>


         <TABLE>
                                                     MAYNARD OIL COMPANY AND SUBSIDIARIES
                                                Consolidated Statements of Shareholders' Equity
                                                     Nine Months Ended September 30, 1998
                                                                  (Unaudited)
         <CAPTION>
                                                                         Additional
                                                   Common Stock           Paid-in
                                                                          Capital        Retained 
                                                Shares      Amount         Amount        Earnings         Total
         <S>                                <C>            <C>          <C>              <C>              <C>
         Balance at December 31, 1997       4,889,450      $488,945     $18,831,138      $34,189,012      $53,509,095 

            Net income                             --            --              --          276,675          276,675 
            Purchase and retirement
              of common stock                  (2,678)         (268)             --          (27,645)         (27,913)

         Balance at September 30, 1998      4,886,772      $488,677     $18,831,138      $34,438,042      $53,757,857 

                                                                                         
          See accompanying Notes to Consolidated Financial Statements.

     </TABLE>


     <TABLE>
                           MAYNARD OIL COMPANY AND SUBSIDIARIES
                          Consolidated Statements of Cash Flows

     <CAPTION>
                                                Nine Months Ended September 30,
                                                         1998          1997
     <S>                                               <S>          <S>
     Cash flows from operating activities:
        Net income                                     $ 276,675    $4,401,074 
        Adjustments to reconcile net income to net
           cash provided by operating activities: 

           Depreciation and amortization               5,391,277     5,268,165 
           Deferred income taxes                         200,000       305,000 
           Dry holes and abandonments                     13,305       447,821 
           Current year costs of dry holes   
             and abandonments                            (13,305)     (447,821)
           (Gain) on disposition of assets                (6,390)     (204,524)
           (Increase) decrease in current assets:
             Accounts receivable                         146,015       943,772 
             Other current assets                        (65,748)     (389,390)
           Increase (decrease) in current liabilities:
             Accounts payable                         (1,738,446)     (615,245)
             Accrued expenses                            383,721       795,100 
             Income taxes payable                       (179,999)   (2,891,242)

             Net cash provided by operating
               activities                              4,407,105     7,612,710 

     Cash flows from investing activities:
        Proceeds from disposition of assets               28,337       276,089 
        Additions to property and equipment           (1,392,814)   (2,562,775)

             Net cash provided (used) by
               investing activities                   (1,364,477)   (2,286,686)

     Cash flows from financing activities:
        Principal payments on long-term debt          (3,750,000)   (3,750,000)
        Purchase of common stock                         (27,913)       --     

             Net cash provided (used) by
               financing activities                   (3,777,913)   (3,750,000)

     Net increase (decrease) in cash and
        cash equivalents                                (735,285)    1,576,024 

     Cash and cash equivalents at beginning
        of year                                       24,584,288    21,817,447 

     Cash and cash equivalents at end of period      $23,849,003   $23,393,471 


     See Accompanying Notes to Consolidated Financial Statements.

     </TABLE>


                          MAYNARD OIL COMPANY AND SUBSIDIARIES
                       Notes to Consolidated Financial Statements
                                   September 30, 1998

     1.   In the opinion of management, the accompanying unaudited  consolidated
          financial  statements  contain  all  adjustments,  consisting  of  all
          recurring  adjustments,  necessary  to  present  fairly  the Company's
          financial  position as of  September 30,  1998 and  December 31, 1997,
          the results  of operations  for the  nine months  ended September  30,
          1998 and 1997 and  changes in cash and  cash equivalents for  the nine
          months ended September 30, 1998 and 1997.

          The accounting policies followed by the Company are set  forth in Note
          1 to the Company's  financial statements in the 1997 Annual Report  to
          Shareholders.

     2.   Net  income  for the  nine  months  ended  September 30,  1998  is not
          necessarily indicative  of the  results of the  operations of  Maynard
          Oil Company  and Subsidiaries for the  year ending  December 31, 1998,
          and is subject to audit adjustments at year-end.

     3.   Net  income per common share  is based on  the weighted average number
          of  shares  outstanding  in  each  period,  which  was  4,888,652  and
          4,889,450 shares at September 30, 1998 and 1997, respectively.

     4.   The provision for income  taxes consists of  the following  (thousands
          of dollars):

                         Nine Months Ended     Three Months Ended 
                           September 30,          September 30,
                         1998        1997        1998       1997 

          Current      $ (115)      $1,283      $(180)     $  68 
          Deferred        200          305        150         50 
                       $   85       $1,588      $ (30)     $ 118 



     MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF
     OPERATIONS

          At  December 31,1997,  the weighted  average product  prices of $15.72
     per  barrel for  crude oil  and $2.05  per thousand  cubic feet  (mcf) for
     natural  gas  were applied  to  the estimates  of  recoverable hydrocarbon
     reserves  to  arrive  at  future  net  revenues  that  the  Company  might
     ultimately  receive.  At that  time, the Company  recognized an impairment
     loss on certain properties whose investment would not be recoverable under
     the above  pricing scenarios  in accordance  with  Statement of  Financial
     Accounting Standards No.  121 ("SFAS 121"), Accounting  for the Impairment
     of Long Lived Assets  and for Long-Lived Assets to be Disposed of.  During
     the  first nine months of  1998, the Company's  hydrocarbon sales averaged
     $12.93 per barrel for crude oil and $2.17 per  mcf for natural gas.  NYMEX
     crude  oil pricing  estimates for  December, 1998  contracts  vary between
     $13.84  and $14.20 per barrel, and  Henry Hub estimates for December, 1998
     natural gas contracts vary between  $2.44 and $2.57 per mcf.   The Company
     believes it has made adequate provision for depreciation and  amortization
     expense in its September  30, 1998 financial statements, but  should crude
     oil prices remain at  current levels, an additional impairment  loss could
     be recognized in the fourth quarter. 

     Nine  Months  Ended  September 30,  1998  Compared  to  Nine Months  Ended
     September 30, 1997

          The  Company reported net income  of $246,675, or six cents per share,
     on revenues  of $13,739,095 for  the nine months ended  September 30, 1998
     compared with  net income  of $4,401,074, or  ninety cents  per share,  on
     revenues of $21,068,438 for the same period a year ago.   Earnings for the
     1998 period were adversely  affected by the sharp reduction in oil prices,
     and to a lesser extent,  by production declines in the volumes  of oil and
     gas  sold.   Gas volumes  dropped almost 16%  from a  year ago,  while oil
     volumes declined almost 7% over the same period.  Crude oil prices plunged
     $6.71  per barrel  between  the two  nine  month periods,  and  gas prices
     declined  thirty-three cents  per mcf.   Thus,  oil and gas  revenues were
     $7,276,847 less than nine months a year ago, a 36% reduction.

          Operating  expenses  reflected  a  decrease of  $1,067,330,  primarily
     attributable to lower severance taxes.

          Exploration costs, which  include dry holes and abandonments,  dropped
     $391,267 between the two nine month periods.  During the 1997 nine months,
     the  Company participated in two seismic shoots and drilled an exploratory
     dry hole, but  during the  current period the  exploratory costs  incurred
     were to complete earlier projects.

          General and administrative expense declined $124,801, almost 15%,  due
     to increased  overhead billings on Company operated  properties, which are
     recorded as reductions to general and administrative  expense.

          Interest expense decreased over 24% between  the prior period and  the
     current nine months due to scheduled debt payments.
     Quarter Ended September 30, 1998 Compared with Quarter Ended September 30,
     1997

          For the quarter ended September 30,  1998, the Company earned $48,473,
     or one cent per share, compared with net income of  $1,430,864, or twenty-
     nine cents per  share, for the  same quarter a year  ago. Results for  the
     current quarter were,  once again,  driven by  lower oil  and gas  prices.
     Revenues from sales were $2,123,456 below the same quarter a year ago.
     Liquidity and Capital Resources

          At September 30, 1998, the Company s  primary source of liquidity  was
     $23,849,003  in cash and marketable  securities.  Historically,   the cash
     generated by operating activities and  proceeds from bank borrowings  have
     been  utilized  to  finance  the  growth  of  the  Company.   The  Company
     anticipates  utilizing  the  same  strategy  to  finance  future  property
     acquisitions and planned development and exploratory work.
     Year 2000 Issues

          The "Year  2000 Issue" is  the result of computer  programs that were
     written using two  digits rather than four to  define the applicable year.
     Any systems developed with this methodology could  fail to operate or fail
     to produce correct  results if  "00" is interpreted  to mean 1900,  rather
     than 2000.

          In  response to the  potential impact of  the Year 2000  issue on the
     Company's business  and operations,  certain Company executives  have been
     appointed  to serve  on its  Year 2000  Readiness Team.   This  group will
     inventory and assess the readiness for Year 2000 compliance by the Company
     and  its  vendors, suppliers,  customers  and  other significant  business
     relationships.

          In  1990, as  part of  a business  modernization program  intended to
     reduce cycle time and  improve profitability, the Company purchased  a new
     accounting  package which  runs on  PC and  LAN platforms.   The  software
     vendor  has  provided  written assurance  that  dating  changes have  been
     throughly tested and were found to be functioning correctly.   The Company
     will  conduct further testing of  this system, along  with other ancillary
     financial  systems,  during the  second  quarter of  1999  and anticipates
     completion by  September 30, 1999.   The costs of these  efforts have been
     funded by cash flow from operations.

          The Company  is  in the  data  gathering phase  with  regard to  non-
     financial software and embedded chip technology.  Further activity in this
     area  involves implementing  software upgrades  to selected  equipment and
     verifying Year  2000 compliance.   The Company  anticipates completion  of
     these activities by the end of the third quarter of 1999.

          Additionally,  the  Company  is in  the  process  of identifying  and
     contacting  critical suppliers,  vendors, and  customers to  determine the
     extent  to which the Company's  interface systems are  vulnerable to those
     third parties'  failure to  remedy  their own  Year 2000  issues.   It  is
     expected that full identification will be  completed by June 30, 1999.  To
     the   extent   that   responses   regarding  Year   2000   readiness   are
     unsatisfactory,   the  Company   intends  to   change  external   business
     relationships to those who have demonstrated Year 2000 readiness.

          Given  the  complexity of  the  Year  2000  issue,  there can  be  no
     assurance that the Company will be able to  address these problems without
     costs  and uncertainties  that might  affect  future financial  results or
     cause  reported financial information not  to necessarily be indicative of
     future operating results or future financial condition.


                             PART II.  OTHER INFORMATION

     ITEM 6.   Exhibits and Reports on Form 8-K

               (a)  Exhibits:
                    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.


                                        MAYNARD OIL COMPANY


                                        By: /s/ Glenn R. Moore
                                                Glenn R. Moore
                                                President


                                        By: /s/ Kenneth W. Hatcher
                                                Kenneth W. Hatcher
                                                Vice President of Finance


     Dated:  November 13, 1998