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, 1999      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, 1999.


               4,883,502 shares of common stock, par value $0.10 











<PAGE>



                       MAYNARD OIL COMPANY AND SUBSIDIARY

            Index to Consolidated Financial Statements and Schedules


                                                                            Page

Part I.  Financial Information

         Consolidated Balance Sheets
                  March 31, 1999 and December 31, 1998                        3

         Consolidated Statements of Operations
                  Three Months ended March 31, 1999 and 1998                  4

         Consolidated Statements of Shareholders' Equity
                  Three Months ended March 31, 1999                           5

         Consolidated Statements of Cash Flows
                  Three Months ended March 31, 1999 and 1998                  6

         Notes to Consolidated Financial Statements                           7

         Management's Discussion and Analysis of Financial
                  Condition and Results of Operations                         8

Signatures                                                                   11


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                       MAYNARD OIL COMPANY AND SUBSIDIARY
                           Consolidated Balance Sheets

                                               March 31,      December 31,
                                                 1999            1998
                                             (Unaudited)       (Audited)
ASSETS
Current assets:
   Cash and cash equivalents                $  20,702,737    $  20,889,742
   Accounts receivable, trade                   2,383,819        2,568,807
   Income taxes receivable                        987,587          977,587
   Other current assets                           492,468          478,680
                                            -------------    -------------
           Total current assets                24,566,611       24,914,816
                                            -------------    -------------
Property and equipment, at cost:
   Oil and gas properties, successful
     efforts method                           107,380,610      107,292,314
   Other property and equipment                   460,475          460,475
                                            -------------    -------------
                                              107,841,085      107,752,789
   Less accumulated depreciation and
     amortization                             (74,514,041)     (72,985,138)
                                            -------------    -------------
        Net property and equipment             33,327,044       34,767,651
                                            -------------    -------------

Deferred income taxes                             711,000          681,000
                                            -------------    -------------
                                            $  58,604,655    $  60,363,467
                                            =============    =============
LIABILITIES AND SHAREHOLDERS' EQUITY
Current liabilities:
   Current installments of long-term debt   $   5,000,000    $   5,000,000
   Accounts payable                             1,815,970        2,583,357
   Accrued expenses                             1,188,056          842,368
   Income taxes payable                            40,799           40,799
                                            -------------    -------------
           Total current liabilities            8,044,825        8,466,524
                                            -------------    -------------

Long-term debt                                  5,000,000        6,250,000

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;
     4,883,502 and 4,884,597 shares
     issued and outstanding                       488,350          488,460
   Additional paid-in capital                  18,831,138       18,831,138
   Retained earnings                           26,240,342       26,327,345
                                            -------------    -------------
           Total shareholders' equity          45,559,830       45,646,943
                                            -------------    -------------

Contingencies and commitments               $  58,604,655    $  60,363,467
                                            =============    =============

See accompanying Notes to Consolidated Financial Statements.




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                       MAYNARD OIL COMPANY AND SUBSIDIARY
                      Consolidated Statement of Operations


                                             Three Months ended March 31,
                                                1999            1998
Revenues:
     Oil and gas sales and royalties         $ 3,435,148    $ 4,689,874
     Interest and other                          246,968        337,966
     Gain on disposition of assets                  --            2,420
                                             -----------    -----------
                                               3,682,116      5,030,260
                                             -----------    -----------

Costs and expenses:
   Operating expenses                          1,792,373      2,316,884
     Exploration, dry holes
       and abandonments                            8,178         15,951
     General and administrative                  289,932        319,913
     Depreciation and amortization             1,537,915      1,791,958
     Interest and other                          171,280        272,719
                                             -----------    -----------
                                               3,799,678      4,717,425
                                             -----------    -----------

         Income (loss) before income taxes      (117,562)       312,835
                                             -----------    -----------
Income tax expense (benefit)                     (40,000)       105,000
                                             -----------    -----------

         Net income (loss)                   $   (77,562)   $   207,835
                                             ===========    ===========

Weighted average number of common shares
   outstanding                                 4,884,082      4,889,442
                                             ===========    ===========
Net income (loss) per common share           $      (.02)   $       .04
 (basic and diluted)                         ===========    ===========
 

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<PAGE>


<TABLE>

                                                   MAYNARD OIL COMPANY AND SUBSIDIARY
                                             Consolidated Statements of Shareholders' Equity
                                                    Three Months Ended March 31, 1999
                                                               (Unaudited)

<CAPTION>

                                                                     Additional
                                             Common Stock              Paid-in
                                                                       Capital         Retained
                                         Shares         Amount         Amount          Earnings         Total

     <S>                               <C>          <C>             <C>            <C>             <C>
     Balance at December 31,1998       4,884,597    $    488,460    $ 18,831,138   $ 26,327,345    $ 45,646,943

          Net (loss)                        --              --              --          (77,562)        (77,562)

          Purchase and retirement
          of common stock                 (1,095)           (110)           --           (9,441)         (9,551)
                                    ------------    ------------    ------------   ------------    ------------

     Balance at March 31, 1999         4,883,502    $    488,350    $ 18,831,138   $ 26,240,342    $ 45,559,830
                                    ============    ============    ============   ============    ============


 See accompanying Notes to Consolidated Financial Statements.

</TABLE>

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<TABLE>

                                               MAYNARD OIL COMPANY AND SUBSIDIARY
                                              Consolidated Statements of Cash Flows

<CAPTION>

                                                            Three Months Ended March 31,
                                                           1999                     1998

<S>                                                    <C>                     <C>         
Cash flows from operating activities:
     Net income (loss)                                 $    (77,562)           $    207,835
     Adjustments to reconcile net income (loss)to
         net cash provided by operating activities:

         Depreciation and amortization                    1,537,915               1,791,958
         Deferred income taxes                              (30,000)                 25,000
         Exploration, dry holes and abandonments              4,905                   6,300
         Current year costs of dry holes and
           abandonments                                      (1,900)                 (6,300)
         (Gain) on disposition of assets                       --                    (2,420)
         (Increase) decrease in current assets:
           Accounts receivable                              184,988                 402,875
           Income taxes receivable                          (10,000)                   --
           Other current assets                             (13,788)                (49,435)
         Increase (decrease) in current liabilities:
           Accounts payable                                (767,387)               (669,904)
           Accrued expenses                                 345,688                 250,291
           Income taxes payable                                --                      --   
                                                       ------------            ------------
           Net cash provided by operating
             activities                                   1,172,859               1,956,200
                                                       ------------            ------------
Cash flows from investing activities:
     Proceeds from disposition of assets                       --                    11,962
     Additions to property and equipment                   (100,313)               (431,495)
                                                       ------------            ------------

           Net cash provided (used) by
             investing activities                          (100,313)               (419,533)
                                                       ------------            ------------

Cash flows from financing activities:
     Principal payments on long-term debt                (1,250,000)             (1,250,000)
     Purchase of common stock                                (9,551)                   (845)
                                                       ------------            ------------

           Net cash provided (used) by
               financing activities                      (1,259,551)             (1,250,845)
                                                       ------------            ------------

Net increase (decrease) in cash and cash
   equivalents                                             (187,005)                285,822

Cash and cash equivalents at beginning of year           20,889,742              24,584,288
                                                       ------------            ------------
Cash and cash equivalents at end of period             $ 20,702,737            $ 24,870,110
                                                       ============            ============

See Accompanying Notes to Consolidated Financial Statements.

</TABLE>

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                       MAYNARD OIL COMPANY AND SUBSIDIARY
                   Notes to Consolidated Financial Statements
                                 March 31, 1999


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, 1999 and December 31, 1998, the results of operations for
     the three months ended March 31, 1999 and 1998 and changes in cash and cash
     equivalents for the three months ended March 31, 1999 and 1998.

     The accounting policies followed by the Company are set forth in Note 1 to
     the Company's financial statements in the 1998 Annual Report to
     Shareholders.

2.   Net income for the three months ended March 31, 1999 is not necessarily
     indicative of the results of the operations of Maynard Oil Company and
     Subsidiary for the year ending December 31, 1999, 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 4,884,082 and 4,889,442 shares
     at March 31, 1999 and 1998, respectively.

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


                              Three Months Ended
                                   March 31      
                               1999       1998
                               ----       ----
            Federal:
               Current        $ (10)     $   80
               Deferred         (30)         25
                              -----      ------
                              $ (40)     $  105
                              =====      ======



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<PAGE>



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

Quarter Ended March 31, 1999 Compared to Quarter Ended March 31, 1998

         The Company reported a net loss of $77,562, or a loss of two cents per
share, on revenues of $3,682,116 for the quarter ended March 31, 1999 compared
with net income of $207,835, or earnings of four cents per share, on revenues of
$5,030,260 for the same quarter a year ago. Results for the first quarter of
1999 were adversely affected by lower revenues. Oil and gas revenues declined
$1,254,726, or almost 27% between the first quarter of 1999 and the first
quarter a year ago, primarily due to lower prices received for its hydrocarbon
products. Oil prices declined an average of $2.95 per barrel from $14.39 to
$11.44 per barrel, and gas prices fell from $2.24 per mcf to $1.90 per mcf.
Lower production volumes also contributed to reduced revenues for the current
quarter with oil volumes falling in excess of 9% and gas volumes approximately
8% as the Company restricted production from certain properties in anticipation
of rising prices. Interest income was approximately $91,000 less during the
first quarter of 1999 due to a decrease in the Company's cash balance of
approximately $4,167,000 over the past year and the resulting amount of cash
available for investment.

         Lower revenues were offset by reduced lease operating expense and
interest costs as well as lower depreciation and amortization expense. Lease
operating costs fell from $7.01 per net equivalent barrel (NEB) during the 1998
quarter to $5.97 per NEB currently due to cost saving measures in field
operations and lower severance taxes. Interest expense was approximately
$101,000 less than the corresponding quarter a year ago due to scheduled note
payments and the resulting lower

                                       -8-

<PAGE>



principal balance outstanding. Depreciation and amortization expense decreased
from $5.42 per NEB during the first quarter of 1998 to $5.12 per NEB in the
current quarter due to a lower amount of net book value remaining after the 1998
non-cash impairment charge to oil and gas properties of $8,700,000.

         An additional tax benefit of $40,000 was recognized during the
first quarter of 1999 to reflect the impact of continued low product
prices during the first two months of the current quarter.

Liquidity and Capital Resources

         The Company ended the first quarter of 1999 with working capital of
approximately $16,521,000 and a current ratio of 3.05 to 1, compared to working
capital of approximately $17,855,000 and a current ratio of 2.70 to 1 a year
ago. The decrease in working capital between the current quarter and the same
period a year ago, $1,334,000, is attributable to the reduction in cash
generated from normal operating activities. At March 31, 1999 the Company's
total debt was $10,000,000. The Company believes that it has sufficient cash on
hand, or additional borrowing capacity, to fund its planned development,
exploratory and acquisition activities.

Year 2000 Issues

         The Company's Year 2000 Readiness Team is continuing to monitor and
evaluate information obtained from vendors, suppliers, customers, and other
significant business relationships with regard to the potential impact of the
century change on the Company's operations. To date, the Company has not
received information suggesting the Company is vulnerable to potential Year 2000
failures by these parties. Testing of the Company's financial systems are
continuing and should be completed by September 30, 1999. The costs associated

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<PAGE>



with assessing Year 2000 readiness and related systems upgrades have been funded
from cash flow from operations and have not been material.

         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.

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET RISK

         None


                                     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.

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<PAGE>




                                   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 14, 1999










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