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   June 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 August 7, 1998.


                 4,888,613 shares of common stock, par value $0.10         


                         MAYNARD OIL COMPANY AND SUBSIDIARY

              Index to Consolidated Financial Statements and Schedules


                                                                 Page

     Part I.   Financial Information

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

          Consolidated Statements of Operations
               Six Months and Three Months ended
               June 30, 1998 and 1997                        

          Consolidated Statements of Shareholders' Equity
               Six Months ended June 30, 1998                

          Consolidated Statements of Cash Flows
               Six Months ended June 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 and Reports on Form 8-K

          Item 4.   Submission of Matters to a Vote of
                    Security Holders


       Signatures

     <TABLE>
                         MAYNARD OIL COMPANY AND SUBSIDIARY
                            Consolidated Balance Sheets
     <CAPTION>
                                                    June 30,     December 31,
                                                     1998            1997    
                                                  (Unaudited)      (Audited) 
     <S>                                          <C>            <C>
     ASSETS
     Current assets:
        Cash and cash equivalents                 $24,550,551    $24,584,288 
        Accounts receivable, trade                  2,910,237      3,267,255 
        Other current assets                          488,123        546,238 
            Total current assets                   27,948,911     28,397,781 

     Property and equipment, at cost:
        Oil and gas properties, successful
          efforts method                          104,676,840    104,031,352 
        Other property and equipment                  547,789        548,668 
                                                  105,224,629    104,580,020 
        Less accumulated depreciation and
         amortization                             (58,286,474)   (54,692,225)
             Net property and equipment            46,938,155     49,887,795 

                                                  $74,887,066    $78,285,576 
     LIABILITIES AND SHAREHOLDERS' EQUITY
     Current liabilities:
        Current installments of long-term debt    $ 5,000,000    $ 5,000,000 
        Accounts payable                            3,122,581      4,271,662 
        Accrued expenses                            1,563,166      1,402,021 
        Income taxes payable                           40,799        220,798 
            Total current liabilities               9,726,546     10,894,481 

     Deferred income taxes                          2,682,000      2,632,000 

     Long-term debt                                 8,750,000     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;
          4,888,613 and 4,889,450 shares
          issued and outstanding                      488,861        488,945 
        Additional paid-in capital                 18,831,138     18,831,138 
        Retained earnings                          34,408,521     34,189,012 
            Total shareholders' equity             53,728,520     53,509,095 

     Contingencies and commitments                $74,887,066    $78,285,576 


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

         <TABLE>
                                                      MAYNARD OIL COMPANY AND SUBSIDIARY
                                                    Consolidated Statements of Operations
         <CAPTION>
                                                                Six Months ended                 Three Months ended
                                                                    June 30,                          June 30,
                                                              1998            1997              1998           1997
         <S>                                              <C>             <C>               <C>            <C>
         Revenues:
              Oil and gas sales                           $ 8,823,345     $13,976,736       $ 4,133,471    $ 6,207,323 
              Interest and other                              677,312         586,924           339,346        314,493 
              Gain on disposition of assets                     9,795          57,292             7,375         55,260 
                                                            9,510,452      14,620,952         4,480,192      6,577,076 

         Costs and expenses:
              Operating expenses                            4,431,297       4,952,188         2,114,413      2,500,111 
              Exploration, dry holes                                  
                and abandonments                               45,310         390,760            29,359        316,512 
              General and administrative                      538,683         661,406           218,770        344,208 
              Depreciation and amortization                 3,616,262       3,492,265         1,824,304      1,792,265 
              Interest and other                              535,698         684,123           262,979        332,597 
                                                            9,167,250      10,180,742         4,449,825      5,285,693 

                Income before income taxes                    343,202       4,440,210            30,367      1,291,383 

         Income tax expense                                   115,000       1,470,000            10,000        435,000 

                Net income                                $   228,202     $ 2,970,210       $    20,367    $   856,383 

         Weighted average number of common
            shares outstanding                              4,889,352       4,889,450         4,889,262      4,889,450 

         Net income per common share                            $.047           $.607             $.004          $.175


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

         <TABLE>
                                                      MAYNARD OIL COMPANY AND SUBSIDIARY
                                               Consolidated Statements of Shareholders' Equity
                                                        Six Months Ended June 30, 1998
                                                                 (Unaudited)
         <CAPTION>

                                                                              Additional           
                                                        Common Stock            Paid-in  
                                                                                Capital           Retained 
                                                    Shares        Amount         Amount           Earnings           Total    
         <S>                                      <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                               --            --               --          228,202           228,202 

                Purchase of common stock               (837)          (84)              --           (8,693)           (8,777)

          Balance at June 30, 1998                4,888,613      $488,861      $18,831,138      $34,408,521       $53,728,520 

                                                                                          
          See accompanying Notes to Consolidated Financial Statements.

         </TABLE>


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

     <CAPTION>
                                                     Six Months Ended June 30,
                                                          1998       1997
     <S>                                                <C>        <C>
     Cash flows from operating activities:
        Net income                                      $ 228,202  $2,970,210 
        Adjustments to reconcile net income to net
          cash provided by operating activities: 

          Depreciation and amortization                 3,616,262   3,492,265 
          Deferred income taxes                            50,000     255,000 
          Dry holes and abandonments                        8,554     390,760 
          Current year costs of dry holes and   
            abandonments                                   (8,554)   (390,760)
          (Gain) on disposition of assets                  (9,795)    (57,292)
          (Increase) decrease in current assets:
            Accounts receivable                           357,018   1,104,895 
            Prepaid expenses and other current assets      58,115     (31,425)
          Increase (decrease) in current liabilities:
            Accounts payable                           (1,149,081)   (556,346)
            Accrued expenses                              161,145     372,685 
            Income taxes payable                         (179,999) (3,326,239)

            Net cash provided by
              operating activities                      3,131,867   4,223,753 

     Cash flows from investing activities:
        Proceeds from disposition of assets                19,334      65,662 
        Additions to property and equipment              (676,161) (1,900,379)

            Net cash provided (used) by
              investing activities                       (656,827) (1,834,717)

     Cash flows from financing activities:
        Purchase of common stock                           (8,777)      --    
        Principal payments on long-term debt           (2,500,000) (2,500,000)

            Net cash provided (used) by
              financing activities                     (2,508,777) (2,500,000)

     Net increase (decrease) in cash and cash
        equivalents                                       (33,737)   (110,964)

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

     Cash and cash equivalents at end of period       $24,550,551 $21,706,483 


     See Accompanying Notes to Consolidated Financial Statements.

     </TABLE>


                         MAYNARD OIL COMPANY AND SUBSIDIARY
                     Notes to Consolidated Financial Statements
                                   June 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  June   30,  1998  and
          December 31, 1997,  the results  of  operations for  the six  months
          ended  June  30,  1998  and  1997  and  changes  in  cash  and  cash
          equivalents for the six months ended June 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 six months ended June 30, 1998 is not necessarily
          indicative of the results  of the operations of Maynard  Oil Company
          and Subsidiary for the year ending December 31, 1998, and is subject
          to audit adjustments at year-end.

     3.   Net income (loss) per common share is  based on the weighted average
          number  of shares outstanding in  each period, which  was  4,889,352
          and 4,889,450 shares at June 30, 1998 and 1997, respectively.

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

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

          Federal:
             Current            $  65    $1,215     $ (15)     $ 315  
             Deferred (benefit)    50       255        25        120  

                                $ 115    $1,470     $  10      $ 435  



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

     Overview

          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 all 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 six months of  1998, the Company's  hydrocarbon sales averaged
     $13.35 per barrel for crude oil and $2.23 per mcf for natural gas.  NYMEX
     crude oil pricing  estimates for  December, 1998  contracts vary  between
     $14.78 and  $15.71 per barrel, and Henry Hub estimates for December, 1998
     natural gas  contracts vary between $2.46 and $2.66 per mcf.  The Company
     believes it has made adequate provision for depreciation and amortization
     expense in its June 30,  1998 financial statements, but should crude  oil
     prices remain at current  levels, an additional impairment loss  could be
     recognized in future periods. 

     Six Months Ended June 30, 1998 Compared to Six Months Ended June 30, 1997

         The Company reported net income of $228,202, or five cents per share,
     on revenues of $9,510,452 for the six months ended June 30, 1998 compared
     with net income of $2,970,210, or sixty-one cents  per share, on revenues
     of $14,620,952 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
     produced and sold.  Gas volumes dropped almost 14% from a year ago, while
     oil  volumes fell slightly in  excess of 5% over  the same period.  Crude
     oil prices  plunged $7.24 per  barrel between the two  six month periods,
     and gas  prices declined  forty-nine cents  per mcf.   Thus, oil  and gas
     revenues were $5,153,391 less than six months a year ago, a 37% decline.

         Operating  expenses  reflected  a  decrease  of  $520,891,  primarily
     attributable to lower  severance taxes  from reduced oil  and gas  sales.
     When  converted to a net equivalent barrel basis ( NEB ,  conversion of 6
     mcf  equal to 1 NEB), the amounts are similar - $6.71 per NEB during 1998
     compared to $6.95 per NEB in 1997.

               Exploration costs,  which include  dry holes  and abandonments,
     dropped $345,450  between the two six month periods.  During the 1997 six
     months,  the Company  participated  in a  seismic  shoot and  drilled  an
     exploratory dry hole, but during  the current period, minimal exploratory
     costs were expended to complete earlier projects.

               General and  administrative expenses declined  $122,723, almost
     19%,  to   reflect  lower  phantom   stock  expense  (which   relates  to
     fluctuations in the Company's common stock  price) and increased overhead
     billings on Company operated properties, which are recorded as reductions
     to administrative expense.

               Depreciation and  amortization expense rose $123,997 during the
     current six months (from $4.90  per NEB for the 1997 period  to $5.48 per
     NEB currently).  Expressed as a percentage of net book value, the overall
     depletion and amortization rate rose from 6.2% in 1997 to 7.2% in 1998.

               Interest  expense  decreased   $148,425  in  the   1998  period
     reflecting  reductions in  outstanding  bank debt  due to  scheduled loan
     repayments.

     Quarter Ended June 30, 1998 Compared with Quarter Ended June 30, 1997

               For  the  quarter  ended  June  30,  1998,  the  Company earned
     $20,367, or less than a half cent per share, compared with  net income of
     $856,383, or eighteen cents per  share, for the same quarter a  year ago.
     The  current quarter s results were adversely affected by the precipitous
     drop in  oil prices  during the  second quarter of  1998 compared  to the
     second quarter of 1997.   Oil prices for the current quarter  were $12.32
     compared to $18.54 for the same quarter a year ago.
     Liquidity and Capital Resources

         The Company ended  its first six months of 1998  with working capital
     of $18,222,365 compared  to working  capital of $15,267,815  a year  ago.
     The improvement in working capital is attributable to cash generated from
     normal operating activities. At  June 30, 1998, the Company's  total debt
     was $13,750,000.   The Company believes that it has sufficient cash being
     generated from operating activities  plus cash currently in the  bank, or
     additional  borrowing  capacity,  to  fund its  planned  development  and
     exploratory work or to make future property acquisitions.

                            PART II.  OTHER INFORMATION

     ITEM 4.   Submission of Matters to a Vote of Security Holders

               (a)  The Annual  Meeting of Stockholders  was held  on May  20,
                    1998.

               (b)  Not applicable.


               (c)  1. Set forth  below is the tabulation of the votes on each
                       nominee for election of a director:

                                                             WITHHOLD 
                       NAME                      FOR         AUTHORITY

                    Ralph E. Graham           4,651,940        4,090  
                    Robert B. McDermott       4,651,940        4,090  
                    James G. Maynard          4,651,940        4,090  

                    2. Not applicable.


     ITEM 6.   Exhibit 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 and  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: August 7, 1998