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   March 31, 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 May 7, 1998.


                4,889,369 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
          March 31, 1998 and December 31,1997           

     Consolidated Statements of Operations
          Three Months ended March 31, 1998 and 1997    

     Consolidated Statements of Shareholders' Equity
          Three Months ended March 31, 1998             

     Consolidated Statements of Cash Flows
          Three Months ended March 31, 1998 and 1997 

     Notes to Consolidated Financial Statements

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

Signatures


<TABLE>
                       MAYNARD OIL COMPANY AND SUBSIDIARY
                           Consolidated Balance Sheets
<CAPTION>
                                             March 31,  
                                                           December 31,
                                               1998            1997    
                                            (Unaudited)      (Audited) 
<S>                                        <C>            <C>
ASSETS
Current assets:
   Cash and cash equivalents               $ 24,870,110   $ 24,584,288 
   Accounts receivable, trade                 2,864,380      3,267,255 
   Other current assets                         595,673        546,238 
       Total current assets                  28,330,163     28,397,781 

Property and equipment, at cost:
   Oil and gas properties, successful
     efforts method                         104,445,132    104,031,352 
   Other property and equipment                 534,829        548,668 
                                            104,979,961    104,580,020 
   Less accumulated depreciation and
     amortization                           (56,462,171)   (54,692,225)
        Net property and equipment           48,517,790     49,887,795 

                                           $ 76,847,953   $ 78,285,576 
LIABILITIES AND SHAREHOLDERS' EQUITY
Current liabilities:
   Current installments of long-term debt   $ 5,000,000    $ 5,000,000 
   Accounts payable                           3,601,758      4,271,662 
   Accrued expenses                           1,652,312      1,402,021 
   Income taxes payable                         220,798        220,798 
       Total current liabilities             10,474,868     10,894,481 

Deferred income taxes                         2,657,000      2,632,000 

Long-term debt                               10,000,000     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;
     4,889,369 and 4,889,450 shares
     issued and outstanding                     488,937        488,945 
   Additional paid-in capital                18,831,138     18,831,138 
   Retained earnings                         34,396,010     34,189,012 
       Total shareholders' equity            53,716,085     53,509,095 

Contingencies and commitments              $ 76,847,953   $ 78,285,576 


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



<TABLE>
                       MAYNARD OIL COMPANY AND SUBSIDIARY
                      Consolidated Statement of Operations

<CAPTION>

                                        Three Months ended March 31,
                                            1998            1997    
<S>                                      <C>            <C>
Revenues:
   Oil and gas sales and royalties        $4,689,874     $7,769,413 
   Interest and other                        337,966        272,431 
   Gain on disposition of assets               2,420          2,032 
                                           5,030,260      8,043,876 

Costs and expenses:
   Operating expenses                      2,316,884      2,452,077 
   Exploration, dry holes
     and abandonments                         15,951         74,248 
   General and administrative                319,913        317,198 
   Depreciation and amortization           1,791,958      1,700,000 
   Interest and other                        272,719        351,526 
                                           4,717,425      4,895,049 

     Income before income taxes              312,835      3,148,827 

Income tax expense                           105,000      1,035,000 
     
     Net income                           $  207,835     $2,113,827 

Weighted average number of common
   shares outstanding                      4,889,442      4,889,450 

Net income per common share                   $ .04          $ .43

</TABLE>



<TABLE>
                                                   MAYNARD OIL COMPANY AND SUBSIDIARY
                                             Consolidated Statements of Shareholders' Equity
                                                    Three Months Ended March 31, 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                              --            --               --                 207,835            207,835 

        Purchase and retirement
        of common stock                          (81)           (8)            --                    (837)              (845)

 Balance at March 31, 1998                 4,889,369      $488,937        $18,831,138         $34,396,010        $53,716,085 

                                                                                     
 See accompanying Notes to Consolidated Financial Statements.

</TABLE>



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

                                                                           
                                               Three Months Ended March 31,
                                                      1998        1997
<S>                                               <C>           <C>
Cash flows from operating activities:
   Net income                                     $  207,835    $2,113,827 
   Adjustments to reconcile net income to net
     cash provided by operating activities: 

     Depreciation and amortization                 1,791,958     1,700,000 
     Deferred income taxes                            25,000       135,000 
     Exploration, dry holes and abandonments           6,300          --   
     Current year costs of dry holes and   
       abandonments                                   (6,300)         --   
     (Gain) on disposition of assets                  (2,420)       (2,032)
     (Increase) decrease in current assets:
       Accounts receivable                           402,875       802,967 
       Prepaid expenses and other current assets        
                                                     (49,435)       52,750 
     Increase (decrease) in current liabilities:
       Accounts payable                             (669,904)     (391,200)
       Accrued expenses                              250,291       215,477 
       Income taxes payable                            --       (2,491,241)

       Net cash provided by operating
         activities                                1,956,200     2,135,548 

Cash flows from investing activities:
   Proceeds from disposition of assets                11,962         2,032 
   Additions to property and equipment              (431,495)     (722,561)

       Net cash used by investing
         activities                                 (419,533)     (720,529)

Cash flows from financing activities:
   Principal payments on long-term debt           (1,250,000)   (1,250,000)
   Purchase of common stock                             (845)        --    

       Net cash used by financing
         activities                               (1,250,845)   (1,250,000)

Net increase in cash and cash equivalents            285,822       165,019 

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

Cash and cash equivalents at end of period       $24,870,110   $21,982,466 


See Accompanying Notes to Consolidated Financial Statements.

</TABLE>


                       MAYNARD OIL COMPANY AND SUBSIDIARY
                   Notes to Consolidated Financial Statements
                                 March 31, 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 March 31, 1998 and December 31,1997, the results of operations for
     the three months ended March 31, 1998 and 1997 and changes in cash and cash
     equivalents for the three months ended March 31, 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 three months ended March 31, 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 per common share is based on the weighted average number of
     shares outstanding in each period, which was  4,889,442 and 4,889,450
     shares at March 31, 1998 and 1997, respectively.

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

                                                      Three Months Ended
                                                           March 31
                                                       1998        1997 
          Federal:
             Current                                   $  80     $  900 
             Deferred                                     25        135 
                                                             
                                                       $ 105     $1,035 



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

Quarter Ended March 31, 1998 Compared to Quarter Ended March 31, 1997

    The Company reported net income of $207,835, or four cents per share, on
revenues of $5,030,260 for the quarter ended March 31, 1998 compared with net
income of $2,113,827, or forty-three cents per share, on revenues of $8,043,876
for the same quarter a year ago.  Results for the first quarter of 1998 were
adversely affected by product pricing, which accounts for all of the reduction
in net income between the two periods.  The price of oil and gas dropped almost
37% and 35% respectively, between the first quarters of 1997 and 1998.  Since
the Company's oil and gas prices averaged only $14.39 per barrel and $2.24 per
thousand cubic feet (mcf) during the current quarter versus $22.72 per barrel
and $3.43 per mcf during the same quarter a year ago, it is not surprising that
revenues and earnings suffered.  Company management does not foresee a quick
pricing recovery.  In the meantime, however, they will continue to monitor all
controllable budgeted categories with the goal of maintaining daily operations
within the Company's cash flow parameters.
Liquidity and Capital Resources

    The Company ended the first quarter of 1998 with working capital of
approximately $17,855,000 and a current ratio of 2.7 to 1, compared to working
capital of approximately $14,918,000 and a current ratio of 2.3 to 1 a year
ago.  The increase in working capital between the current quarter and the same
period a year ago, $2,937,000, is attributable to cash generated from normal
operating activities.  At March 31, 1998 the Company's total debt was 
$15,000,000.  The Company believes that it has sufficient cash on hand, or 
additional borrowing capacity, to fund its planned development, exploratory
and acquisition activities.

                                     PART II

ITEM 6:   EXHIBITS AND REPORTS ON FORM 8-K
          (a)  Financial Data Schedule
          (b)  No reports on Form 8-K were filed during the quarter.


                                   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: May 8, 1998