<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D. C. 20549
                                    FORM 10-Q


(Mark One)


[X] Quarterly report pursuant to Section 13 or 15 (d) of the Securities Exchange
    Act of 1934

              For the quarterly period ended September 30, 1998 or


[ ] Transition report pursuant to Section 13 or 15 (d) of the Securities 
    Exchange Act of 1934

         For the transition period from           to
                                        ---------     --------

                          Commission File Number 1-7908
                                                -------

                         ADAMS RESOURCES & ENERGY, INC.
                         ------------------------------
             (Exact name of Registrant as specified in its charter)


             Delaware                               74-1753147
    ------------------------------               ------------------
   (State or other jurisdiction of               (I.R.S. Employer
    incorporation or organization)               Identification No.)


                      5 Post Oak Park, Houston, Texas 77027
               (Address of principal executive office & Zip Code)


        Registrant's telephone number, including area code (713) 881-3600
                                                           --------------
     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  [ ]
                                        ----    ----

The number of shares of Common Stock of the Registrant, par value $.10 per
share, outstanding at October 31, 1998 was 4,217,596.




<PAGE>   2



                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                 UNAUDITED CONSOLIDATED STATEMENT OF OPERATIONS
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)
<TABLE>
<CAPTION>

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

<S>                                                  <C>              <C>              <C>              <C>        
REVENUE:
  Marketing                                          $ 1,394,599      $ 1,358,071      $   533,893      $   440,604
  Transportation                                          24,215           22,915            7,223            8,644
  Oil & Gas                                                4,790            7,044            1,274            2,622
                                                     -----------      -----------      -----------      -----------
                                                       1,423,604        1,388,030          542,390          451,870
                                                     -----------      -----------      -----------      -----------

COSTS AND EXPENSES:
Operating
   Marketing                                         ...1,388,723       1,355,837          532,151          439,403
   Transportation                                         21,317           18,443            6,427            6,997
   Oil & Gas                                               2,659            1,225              720              431
Corporate general and administrative                       1,825            1,618              668              541
Depreciation, depletion and amortization                   6,288            4,814            2,036            2,062
                                                     -----------      -----------      -----------      -----------
                                                       1,420,812        1,381,937          542,002          449,434
                                                     -----------      -----------      -----------      -----------

Operating earnings                                         2,792            6,093              388            2,436

OTHER INCOME (EXPENSE):
Property sales and other                                      78              615              (30)            --
Interest                                                    (268)            (197)            (122)             (69)
                                                     -----------      -----------      -----------      -----------
                                                            (190)             418             (152)             (69)
                                                     -----------      -----------      -----------      -----------

Earnings before income taxes                               2,602            6,511              236            2,367
Income tax provision:
   Current                                                   770              295               68              124
   Deferred                                                  225            2,050               25              675
                                                     -----------      -----------      -----------      -----------
                                                             995            2,345               93              799
                                                     -----------      -----------      -----------      -----------

NET EARNINGS                                         $     1,607      $     4,166      $       143      $     1,568
                                                     ===========      ===========      ===========      ===========

PER COMMON SHARE DATA:
   Basic and diluted net earnings                    $       .38      $       .99      $       .03      $       .37
                                                     ===========      ===========      ===========      ===========

   Dividends                                         $      --        $      --        $      --        $      --
                                                     ===========      ===========      ===========      ===========

</TABLE>


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


                                      -2-


<PAGE>   3
                MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                       CONDITION AND RESULTS OF OPERATIONS


     Results of Operations

Nine Months Comparison

              -  Marketing


              Marketing division revenues and operating earnings were as follows
(in thousands):

<TABLE>
<CAPTION>


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

<S>                                     <C>            <C>             <C>            <C>
Revenues                                $1,394,599     $1,358,071$        533,893     $  440,604

Operating earnings (loss)               $    3,542     $    1,419      $      965     $      878
</TABLE>


              Gross revenues for the Company's Marketing operations increased by
     $36,528,000 or 3%, in the comparative current period as a result of
     increased volumes of crude oil purchased at the wellhead offset by lower
     crude oil prices. Compared to last year, average crude oil sales prices
     were reduced by approximately 38% in 1998 as crude oil fell to the $13 per
     barrel range. Average wellhead purchases were 112,000 barrels per day in
     1998 versus 78,000 barrels per day in 1997. Marketing division operating
     margins for the first nine months of 1998 increased to $3,542,000
     principally because of the reversal of unusually unfavorable market
     conditions that existed in 1997.

              - Transportation

              Transportation revenues and operating earnings were as follows 
(in thousands):
<TABLE>
<CAPTION>

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

<S>                                                <C>         <C>         <C>         <C>    
           Revenues                                $24,215     $22,915     $ 7,223     $ 8,644

           Operating earnings                      $ 2,197     $ 4,002     $   538     $ 1,484

</TABLE>

              Transportation revenues increased in 1998 because recent equipment
     additions enabled the Company to handle a larger volume of business.
     Operating earnings were reduced, however, when 





                                      -3-
<PAGE>   4




     sales volumes did not grow as fast as anticipated due to an apparent
     general slowing of the United States economy. As noted, in order to service
     a larger volume of business, the Company expanded capacity which
     necessitated increased fixed costs. When the rate of sales volume growth
     slowed during 1998, the new higher level of fixed cost caused the earnings
     decline.

              During the third quarter of 1998, the Company experienced a
     generally slowdown in the demand for its services. This caused a revenue
     decline relative to the third quarter of 1997 and also contributed to
     reduced operating earnings.


              - Oil and Gas

              Oil and gas division revenues and operating earnings were as
follows (in thousands):
<TABLE>
<CAPTION>

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

<S>                                                <C>          <C>         <C>          <C>    
           Revenues                                $ 4,790      $ 7,044     $ 1,274      $ 2,622

           Operating earnings (loss)               $(1,122)     $ 2,307     $  (447)     $   615

</TABLE>


              Oil and gas revenues decreased for the comparative nine month
     period as a result of reduced crude oil prices and reduced natural gas
     prices and volumes. Operating earnings in 1998 were also reduced because
     the Company incurred and expensed $1.4 million of 3D seismic costs during
     the first nine months of the year with $360,000 being incurred during the
     third quarter. Volumes and prices compare as follows:


               Volumes and prices compare as follows:
<TABLE>
<CAPTION>

                                              Nine Months Ended                 Three Months Ended
                                       ------------------------------     -----------------------------
                                            1998             1997              1998            1997
                                       -------------     ------------     -------------     -----------

Crude oil
<S>                                   <C>               <C>              <C>               <C>         
   Volume                               56,400 Bbls.       49,300 Bbls.      20,200 Bbls.      17,800 Bbls.
   Average price                      $ 12.90/ Bbl.      $ 20.09/ Bbl.     $ 11.55/ Bbl.     $ 17.86/ Bbl.

Natural gas
   Volume (IN THOUSANDS)                 2,180 Mcf's        2,575 Mcf's         555 Mcf's       1,075 Mcf's
   Average price, includes
     value of associated gas
     liquids                          $  1.90/ Mcf       $  2.33/ Mcf      $  1.86/ Mcf       $ 2.09/ Mcf
</TABLE>





                                      -4-
<PAGE>   5


              - Other income (expense)

              The provision for depreciation, depletion and amortization is
     increased in 1998 because of a larger capitalized cost base. Recently
     included in the depreciable cost base is the Company's offshore Louisiana
     crude oil pipeline completed at a cost of $4.2 million and placed in
     service in January 1998. Property sales and other income for 1998 resulted
     primarily from the sale of a former gasoline service station location while
     1997 included a $401,000 recovery from an insurance carrier for prior year
     overcharges and a $214,000 gain realized on the sale of twenty-one truck
     tractors. Interest expense is increased during 1998 because of a relatively
     higher average level of debt during the period.

Three Months Comparisons

              Comparisons for the three month period ended September 30, 1998
are consistent with the discussions provided above.


     Liquidity and Capital Resources

              During the first nine months of 1998, the Company invested
     $7,534,000 in property additions. Included in the amount invested was $2.8
     million for the purchase of oil and gas producing properties and other oil
     and gas drilling efforts. Approximately $2 million was incurred for
     expansion of the Company's truck terminals and the remaining $2.7 million
     of property additions were for various marketing and transportation
     equipment items. Funding for these investments was derived from the Company
     generating $7,295,000 of working capital funds.

              During 1998, the Company's primary lending bank increased the
     Company's borrowing availability under its oil and gas working capital line
     to $5.5 million. As of September 30, 1998, total available working capital
     borrowing capacity was $9.7 million with $7.8 million outstanding. Refer to
     the "Liquidity and Capital Resources" section of the Company's Annual
     Report on Form 10-K for the year ended December 31, 1997 for additional
     discussion of the Company's bank facilities and other matters.

     Year 2000

         Many currently installed computer systems and software products are
coded to accept only two digit entries in the date code filed. Beginning in the
year 2000, these date code fields will need to accept four-digit entries to
distinguish 21st century dates from 20th century dates. As a result, computer
systems and software used by many companies may need to be upgraded to comply
with such "Year 2000" requirements. Significant uncertainty exists concerning
the potential effects associated with such compliance, but systems that do not
properly recognize such information could generate erroneous data or cause a
system to fail.

         The Company is in the process of implementing certain new operating
computer systems applications necessary to resolve potential year 2000
compliance issues. Many of the Company's operating and financial systems are
already compliant. The Company's remaining operating and financial 



                                      -5-

<PAGE>   6



systems are scheduled for compliance in phases and will be compliant by the year
2000. The Company is communicating with software vendors, business partners and
others with which it conducts business to provide assurances that their systems
will be year 2000 compliant. As of September 30, 1998, the Company had incurred
and expensed approximately $150,000 of costs to become year 2000 compliant. An
additional $50,000 is expected to be incurred and expensed in future periods in
order to complete this project.










                                      -6-



<PAGE>   7


                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>

                                                          September 30,   December 31,
                                                              1998           1997
                                                          -------------   ------------
                                                           (Unaudited)

ASSETS

<S>                                                        <C>            <C>      
Current assets:
  Cash and cash equivalents ...........................     $  10,210      $   6,496
  Accounts receivable, net ............................        70,696         73,806
  Inventories .........................................         5,408          5,092
  Prepaid and other ...................................         1,053          1,675
                                                            ---------      ---------
                Total current assets ..................        87,367         87,069
                                                            ---------      ---------

Property and equipment ................................        63,271         56,298
  Less - accumulated depreciation,
         depletion and amortization ...................       (36,180)       (30,361)
                                                            ---------      ---------
                                                               27,091         25,937
                                                            ---------      ---------


Other assets ..........................................         1,315          1,277
                                                            ---------      ---------
                                                            $ 115,773      $ 114,283
                                                            =========      =========


LIABILITIES AND SHAREHOLDERS' EQUITY

Current liabilities:
  Accounts payable ....................................     $  74,110      $  74,829
  Accrued liabilities .................................         3,732          3,475
  Current maturities of long-term debt ................          --               71
                                                            ---------      ---------
         Total current liabilities ....................        77,842         78,375

Long-term debt, less current maturities ...............         7,800          6,900
Other long-term liabilities ...........................           386            870
                                                            ---------      ---------
                                                               86,028         86,145

Shareholders' equity:
  Preferred stock - $1.00 par value, 960,000 shares
      authorized, none outstanding ....................          --             --
  Common stock - $.10 par value, 7,500,000
      shares authorized, 4,217,596 shares
      outstanding, respectively .......................           422            422
  Contributed capital .................................        11,693         11,693
  Retained earnings since December 31, 1992 ...........        17,630         16,023
                                                            ---------      ---------
         Total shareholders' equity ...................        29,745         28,138
                                                            ---------      ---------
                                                            $ 115,773      $ 114,283
                                                            =========      =========
</TABLE>

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



                                      -7-


<PAGE>   8



                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                 UNAUDITED CONSOLIDATED STATEMENT OF CASH FLOWS
                                 (IN THOUSANDS)
<TABLE>
<CAPTION>

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

<S>                                                             <C>           <C>     
CASH PROVIDED (USED) BY OPERATIONS:
  Net earnings ............................................     $  1,607      $  4,166
  Items of income not requiring (providing) cash -
    Depreciation, depletion and amortization ..............        6,288         4,814
    Deferred income tax provision .........................         --           1,450
    Gain on sale of properties ............................          (78)         (215)
    Other, net ............................................         (522)         (231)
  Decrease (increase) in accounts receivable ..............        3,110          (604)
  Decrease (increase) in inventories ......................         (316)          771
  Decrease (increase) in prepaid and other ................          622           222
  Increase (decrease) in accounts payable .................         (719)       (1,578)
  Increase (decrease) in accrued liabilities ..............          257          (847)
                                                                --------      --------
    Net cash provided (required) by operating activities ..       10,249         7,948
                                                                --------      --------
INVESTING ACTIVITIES:
  Property and equipment additions ........................       (7,534)       (8,495)
  Proceeds from property sales ............................          170           425
                                                                --------      --------
    Net cash provided by (used in) investing activities ...       (7,364)       (8,070)
                                                                --------      --------
FINANCING ACTIVITIES:
Borrowings from bank ......................................          900         1,675
Repayment of debt .........................................          (71)          (64)
  Sales of stock ..........................................         --              62
                                                                --------      --------
    Net cash provided by (used in) financing activities ...          829         1,673
                                                                --------      --------
Increase (decrease) in cash and cash equivalents ..........        3,714         1,551
Cash at beginning of period ...............................        6,496         3.782
                                                                --------      --------
Cash at end of period .....................................     $ 10,210      $  5,333
                                                                ========      ========
Supplemental disclosure of cash flow information:
  Interest paid during the period .........................     $    268      $    197
                                                                ========      ========
  Income taxes paid during the period .....................     $    550      $    867
                                                                ========      ========
</TABLE>



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


                                      -8-
<PAGE>   9



                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                               NOTES TO UNAUDITED
                        CONSOLIDATED FINANCIAL STATEMENTS


Note 1 - Basis of Presentation

         The accompanying condensed financial statements are unaudited but, in
the opinion of the Company's management, include all adjustments (consisting of
normal recurring accruals) necessary for a fair presentation of financial
position at September 30, 1998 and December 31, 1997 and results of operations
and cash flows for the nine months ended September 30, 1998 and 1997. Certain
information and note disclosures normally included in annual financial
statements prepared in accordance with generally accepted accounting principles
have been condensed or omitted pursuant to Securities and Exchange Commission
rules and regulations, although the Company believes the disclosures made are
adequate to make the information presented not misleading. It is suggested these
condensed financial statements be read in conjunction with the financial
statements, and the notes thereto, included in the Company's latest annual
report on Form 10-K. The interim statement of operations is not necessarily
indicative of results to be expected for a full year.

         When used in this document, the words "anticipate", "believe",
"expect", "estimate", "project", and similar expressions are intended to
identify forward-looking statements. Such statements are subject to certain
risks, uncertainties and assumptions. Should one or more of these risks or
uncertainties materialize, or should underlying assumptions prove incorrect,
actual results may vary materially from those anticipated, believed, expected or
projected.


Note 2 - New Accounting Standards

         In February 1997, the Financial Accounting Standards Board ("FASB")
issued Statement of Financial Accounting Standards ("SFAS") No. 128, "Earnings
Per Share", which established new standards for computing and presenting
earnings per share. The provisions of the statement are effective for fiscal
years ending after December 15, 1997, and accordingly, have been adopted in the
accompanying financial statements. Under the provisions of SFAS No. 128, the
presentation of primary earnings per share has been replaced with basic earnings
per share, and fully diluted earnings per share presentations have been replaced
with diluted earnings per share for potentially dilutive securities. Prior
period earnings per share data have been restated. Earnings per share are based
on the weighted average number of shares of common stock and common stock
equivalents outstanding during the period. Such shares outstanding averaged
4,217,596 shares for 1998 and 4,213,596 shares for 1997 for both basic and fully
diluted earnings per share.

         In June 1997, the FASB issued SFAS No. 130, "Reporting Comprehensive
Income", which establishes standards for reporting and display of comprehensive
income and its


                                      -9-

<PAGE>   10





                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES

components in a full set of general-purpose financial statements. The statement
requires (a) classification of items of other comprehensive income by their
nature in a financial statement and (b) display of the accumulated balance of
other comprehensive income separate from retained earnings and additional
paid-in capital in the equity section of a statement of financial position. SFAS
No. 130 is effective for interim periods beginning after December 15, 1997. For
the nine month period and for the quarters ended September 30, 1998, and 1997,
there was no difference between the Company's historical and comprehensive net
income.

         In June 1997, the FASB also issued SFAS No. 131, "Disclosure about
Segments of an Enterprise and Related Information", which establishes standards
for reporting information about operating segments in annual financial
statements and requires that selected information be reported about the
operating segments in interim financial reports issued to the shareholders. It
also establishes standards for related disclosure about products and services,
geographic areas, and major customers. The Company has concluded that its
segment information as currently reported is in compliance with SFAS No. 131 and
as such, adoption has no effect on current or prior period presentations.

         In June 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities". The Statement establishes accounting and
reporting standards requiring that every derivative instrument (including
certain derivative instruments embedded in other contracts) be recorded in the
balance sheet as either an asset or liability measured at its fair value. The
Statement requires that changes in the derivatives fair value be recognized
currently in earnings unless specific hedge accounting criteria are met. Special
accounting for qualifying hedges allows a derivative's gains and losses to
offset related results on the hedged item in the income statement, and requires
that a company must formally document, designate, and assess the effectiveness
of transactions that receive hedge accounting. SFAS 133 is required to be
effective for fiscal years beginning after June 15, 1999 and may be adopted
early. The Company has not yet quantified the impact of adopting SFAS 133.


                           PART II. OTHER INFORMATION
Item 1. - None

Item 2. - None

Item 3. - None

Item 4. - None

Item 6.  Exhibits and Reports on Form 8K
     a.   Exhibits - None.
     b.   Reports on Form 8-K - None.



                                      -10-

<PAGE>   11



                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES




         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.

                                         ADAMS RESOURCES & ENERGY, INC.
                                         (Registrant)



Date:    November 12, 1998

                                         By  /s/ K.S. Adams, Jr.
                                             ---------------------------------
                                             K. S. Adams, Jr.
                                             Chief Executive Officer



                                         By  /s/ Richard B. Abshire
                                            -----------------------------------
                                             Richard B. Abshire
                                             Chief Financial Officer






                                      -11-


<PAGE>   12












                                  EXHIBIT INDEX

<TABLE>
Exhibit
Number             Description
-------            -----------
<S>                    <C>
27*      -         Financial Data Schedule
</TABLE>
------------------------------
*  - Filed herewith