<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 March 31, 1999 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 May 12, 1999 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>

                                                            Three Months Ended
                                                                March 31,
                                                       --------------------------
                                                          1999            1998  
                                                       ----------      ----------
<S>                                                    <C>             <C>       
Revenues:
  Marketing                                            $  515,266      $  406,377
  Transportation                                            7,851           8,663
  Oil and Gas                                                 853           1,596
                                                       ----------      ----------
                                                          523,970         416,636

Costs and expenses:
  Operating
   Marketing                                              513,361         404,473
   Transportation                                           7,233           7,534
   Oil and gas                                                709             302
  Corporate general and administrative                        724             543
  Depreciation, depletion and amortization                  1,786           2,193
                                                       ----------      ----------
                                                          523,813         415,045

Operating earnings                                            157           1,591

Other income (expense)
  Property sales and other                                    666             108
  Interest                                                    (30)            (65)
                                                       ----------      ----------

Earnings before income taxes                                  793           1,634
Income tax provision
  Current                                                      45             494
  Deferred                                                    129             100
                                                       ----------      ----------
                                                              174             594
                                                       ----------      ----------

Net earnings                                           $      619      $    1,040
                                                       ==========      ==========

Basic and diluted net earnings                         $      .15      $      .25
                                                       ==========      ==========
  per common share

Dividends per common share                             $       --      $       --
                                                       ==========      ==========
</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

         -   Marketing

         Marketing division revenues, operating earnings and significant
operating statistics were as follows:

<TABLE>
<CAPTION>

                                                                          First Quarter          First Quarter
                                                                               1999                   1998       
                                                                      --------------------    ----------------------

<S>                                                                    <C>                    <C>            
              Revenues                                                 $ 515,266,000          $   406,377,000

              Operating earnings                                       $   1,074,000          $     1,125,000

              Wellhead Purchases
                    Per day(1)                                               192,000 bbls.            105,000 bbls.

              Average Crude
                    Oil Price                                           $      10.99/bbl.     $         14.52/bbl.
</TABLE>

   (1)   Reflects the volume of crude oil purchased from third parties at the 
         lease level and shipped to market.

         Gross revenues for this division's operations increased by $108,889,000
or 27%, in the comparative current period as a result of increased volumes of
crude oil purchased at the wellhead. While volumes increased, marketing division
operating earnings for the first three months of 1999 were consistent with the
1998 period. Within the crude oil marketplace during 1999, supply and demand
conditions caused a narrowing of per unit gross margins. Hence, operating
earnings did not increase with volumes.

         -   Transportation

         Transportation revenues and operating earnings increased (decreased) as
follows:

<TABLE>
<CAPTION>

                                                                                                              Percentage
                                                               First Quarter        First Quarter              Increase
                                                                   1999                  1998                 (Decrease)
                                                              --------------        -------------           --------------

<S>                                                           <C>                   <C>                     <C> 
              Revenues                                        $    7,851,000        $   8,663,000                (9)%
              Operating earnings                              $      383,000        $     919,000               (58)%
</TABLE>






                                      -3-

<PAGE>   4


         This division's revenues and operating earnings suffered during 1999 as
a result of slowing customer demand. In addition, the Company incurred higher
fixed costs in the first quarter of 1999 because the Company had previously
expanded its infrastructure in anticipation of stronger customer demand. Thus
fixed costs grew faster than demand for the Company's services. Beginning in
late March 1999, the Company has seen improvement in customer demand. As such
demand growth continues, profitability is expected to improve.


         - Oil and Gas

         Oil and gas division revenues and operating earnings are primarily a
function of crude oil and natural gas prices and volumes. The reduction in this
division's revenues and operating earnings is a direct result of reduced
production volumes and prices. Comparative amounts are as follows:

<TABLE>
<CAPTION>

                                                                     First Quarter             First Quarter
                                                                         1999                      1998       
                                                                  -------------------       ---------------------

<S>                                                               <C>                       <C>           
         Revenues                                                 $      853,000            $    1,596,000

         Operating earnings                                       $     (576,000)           $       90,000

         Crude oil
               Volume                                                     10,800 bbls.              17,000 bbls.
               Average price                                      $         9.67/bbl.       $        14.56/bbl.

         Natural gas
               Volume                                                    450,000 mcf               800,000 mcf
               Average price                                      $         1.68 mcf        $         1.70 mcf
</TABLE>



         - Depreciation, depletion, and amortization

         The provision for depreciation, depletion and amortization is reduced
in the current quarter due to lower oil and gas production volumes.

         - Other income (expense)

         Property sales and other income of $666,000 and $108,000, respectively,
resulted primarily from gains realized on the sale of forty-five truck tractors
in 1999 and from the sale of a former gasoline service station location during
1998. Interest expense is reduced in 1999 because the Company used its excess
cash flow to reduce its level of long-term debt.


                                      -4-

<PAGE>   5

Liquidity and Capital Resources

         During the first three months of 1999, the Company invested $866,000 in
property and equipment additions with $522,000 expended toward expansion of the
Company's transportation operations and the remainder going toward various oil
and gas projects and marketing equipment items. Funding for these investments
was derived from the Company generating $1,845,000 of working capital funds. The
$979,000 of excess cash flow generated was applied against the Company's working
capital lines of credit.

         Refer to the "Liquidity and Capital Resources" section of the Company's
Annual Report on Form 10-K for the year ended December 31, 1998 for additional
discussion of the Company's bank relationships 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 field. 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 has completed a review of its key computer systems and is
in the process of implementing certain new operating 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 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. Adams could be adversely affected by the
failure of these unaffiliated companies to adequately address the year 2000
issue. Contingency planning will be included in this assessment to identify
arrangements to mitigate the impact of disruptions from outside sources.

         As of year-end 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 1999 in order to complete
this project.    






                                      -5-

<PAGE>   6



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

<TABLE>
<CAPTION>

                                                             March 31,     December 31,
                                                               1999            1998       
                                                            ----------     ------------
                                                            (Unaudited)

<S>                                                     <C>               <C>         

ASSETS

Current assets:
  Cash and cash equivalents ...........................     $   13,179      $   10,215
  Accounts receivable, net ............................         86,181          73,864
  Inventories .........................................          7,557           8,288
  Prepaid and other ...................................          1,497             801
                                                            ----------      ----------

                Total current assets ..................        108,414          93,168
                                                            ----------      ----------

Property and equipment ................................         63,947          64,019
  Less - accumulated depreciation,
         depletion and amortization ...................        (37,707)        (36,226)
                                                            ----------      ----------
                                                                26,240          27,793
                                                            ----------      ----------


Other assets ..........................................          1,373           1,373
                                                            ----------      ----------
                                                            $  136,027      $  122,334
                                                            ==========      ==========


LIABILITIES AND SHAREHOLDERS' EQUITY

Current liabilities:
  Accounts payable ....................................     $   94,877      $   78,444
  Accrued and other liabilities .......................          4,358           3,869
                                                            ----------      ----------

         Total current liabilities ....................         99,235          82,313

Long-term debt, less current maturities ...............          5,200           9,100
Deferred taxes and other liabilities ..................            917             865
                                                            ----------      ----------
                                                               105,352          92,278

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 .....................................            422             422
  Contributed capital .................................         11,693          11,693
  Retained earnings since December 31, 1992 ...........         18,560          17,941
                                                            ----------      ----------
         Total shareholders' equity ...................         30,675          30,056
                                                            ----------      ----------
                                                            $  136,027      $  122,334
                                                            ==========      ==========
</TABLE>


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


                                      -6-

<PAGE>   7



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

<TABLE>
<CAPTION>

                                                                       Three Months Ended
                                                                            March 31,          
                                                                 ------------------------------
                                                                     1999              1998  
                                                                 ------------      ------------


<S>                                                              <C>               <C>         
CASH PROVIDED (USED) BY OPERATIONS:
  Net earnings .............................................     $        619      $      1,040
  Items of income not requiring (providing) cash-
    Depreciation, depletion and amortization ...............            1,786             2,193
    Deferred income tax provision ..........................              129               100
    Gain on sale of properties .............................             (611)              (59)
    Other, net .............................................              (78)             (132)
  Decrease (increase) in accounts receivable ...............          (12,317)           12,550
  Decrease (increase) in inventories .......................              731             3,556
  Decrease (increase) in prepaid and other .................             (696)              587
  Increase (decrease) in accounts payable ..................           16,433           (16,490)
  Increase (decrease) in accrued liabilities ...............              489              (509)
                                                                 ------------      ------------

    Net cash provided (required) by operating activities ...            6,485             2,836
                                                                 ------------      ------------

INVESTING ACTIVITIES:
  Property and equipment additions .........................             (866)           (2,040)
  Proceeds from property sales .............................            1,245                82
                                                                 ------------      ------------

    Net cash provided by (used in) investing activities ....              379            (1,958)
                                                                 ------------      ------------

FINANCING ACTIVITIES:
  Repayment of debt ........................................           (3,900)           (2,435)
                                                                 ------------      ------------

    Net cash provided by (used in) financing activities ....           (3,900)           (2,435)
                                                                 ------------      ------------

Increase (decrease) in cash and cash equivalents ...........            2,964            (1,557)

Cash at beginning of period ................................           10,215             6,496
                                                                 ------------      ------------

Cash at end of period ......................................     $     13,179      $      4,939
                                                                 ============      ============

Supplemental disclosure of cash flow information:

  Interest paid during the period ..........................     $         30      $         65
                                                                 ============      ============

  Income taxes paid during the period ......................     $         --      $         --
                                                                 ============      ============
</TABLE>



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


                                      -7-

<PAGE>   8



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


Note 1 - Basis of Presentation

         The accompanying condensed consolidated 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 March 31, 1999 and December 31, 1998 and
results of operations and cash flows for the three months ended March 31, 1999
and 1998. 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 that these condensed consolidated 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.

Note 2 - Segment Reporting

         The Company adopted SFAS No. 131, "Disclosures about Segments of an
Enterprise and Related Information" effective January 1, 1998. Under this new
standard, companies are required to report certain information about operating
segments in consolidated statements. Operating segments are determined based on
the method by which management organizes its business for making operating
decisions and assessing performance.










                                      -8-


<PAGE>   9


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

         The Company is primarily engaged in the business of crude oil and
petroleum products marketing, transportation, and oil and gas exploration and
production. Information concerning the Company's various business activities is
summarized as follows (in thousands):

<TABLE>
<CAPTION>

                                                                              Depreci-
                                                                               ation,
                                                         Earnings            Depletion         Property
                                                          (Loss)                and               and
                                                           from                Amorti-         Equipment
                                         Revenues        Operations            zation           Additions    
                                       ------------     ------------         ------------     ------------

<S>                                    <C>              <C>                  <C>              <C>         
For the three months ended
March 31, 1999
   Marketing .....................     $    515,266     $      1,074         $        831     $        212
   Transportation ................            7,851              383                  235              522
   Oil and gas ...................              853             (576)(1)              720              132
                                       ------------     ------------         ------------     ------------
                                       $    523,970     $        881         $      1,786     $        866
                                       ============     ============         ============     ============

For the three months ended
March 31, 1998
   Marketing .....................     $    406,377     $      1,125         $        779     $        828
   Transportation ................            8,663              919                  210              414
   Oil and gas ...................            1,596               90                1,204              798
                                       ------------     ------------         ------------     ------------
           .......................     $    416,636     $      2,134         $      2,193     $      2,040
                                       ============     ============         ============     ============
</TABLE>

(1)   Includes a $666,000 comparative earnings decrease caused by dry hole 
      expense and decreased crude oil and natural gas prices.

         Identifiable assets by industry segment are as follows:

<TABLE>
<CAPTION>

                                                    March 31,      December 31,
                                                      1999             1998        
                                                  ------------     ------------


<S>                                               <C>              <C>         
Marketing ...................................     $     98,140     $     86,510
Transportation ..............................           13,603           13,947
Oil and gas .................................            9,608           10,227
Other .......................................           14,676           11,650
                                                  ------------     ------------
                                                  $    136,027     $    122,334
                                                  ============     ============
</TABLE>

         Intersegment sales are insignificant. Other identifiable assets are
primarily corporate cash, accounts receivable, and properties not identified
with any specific segment of the Company's business. All sales by the Company
occurred in the United States.







                                      -9-

<PAGE>   10


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

         Earnings from operations by segment represent revenues less operating
costs and expenses and depreciation, depletion and amortization and are
reconciled to earnings from operations before income taxes, as follows (in
thousands):

<TABLE>
<CAPTION>

                                                   For the three months ended
                                                          March 31, 1999          
                                                  ------------------------------
                                                      1998              1997 
                                                  ------------      ------------

<S>                                               <C>               <C>         
Earnings from operations ....................     $        881      $      2,134
General and administrative expenses .........             (724)             (543)
Property sales and other ....................              666               108
Interest expense ............................              (30)              (65)
                                                  ------------      ------------
Earnings before income taxes ................     $        793      $      1,634
                                                  ============      ============
</TABLE>

Note 3 - Recent Accounting Pronouncements

         In June 1998, the Financial Accounting Standards Board issued Statement
of Financial Accounting Standards ("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 derivative's fair value be recognized
currently in earnings unless specific hedge accounting criteria are met.
Qualifying hedges allow 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 No. 133 is effective for fiscal years
beginning after June 15, 1999. The standard cannot be applied retroactively but
early adoption is permitted. The Company has not yet determined the impacts of
adopting SFAS No. 133; however, this standard could increase volatility in
earnings and shareholder's equity through other comprehensive income.

         On January 1, 1999 the Company adopted the Emerging Issues Task Force's
(EITF) Issue 98-10, "Accounting for Contracts Involved in Energy Trading and
Risk Management Activities." Issue 98-10 is effective for fiscal years beginning
after December 15, 1998, and requires energy trading contracts (as defined) to
be recorded at fair value on the balance sheet, with the change in fair value
included in earnings. The effect of initial adoption on January 1, 1999 was not
significant. The accompanying statement of operations includes a net charge of
$242,000 to reflect a loss in marketing revenues for the current period relating
to such activities. The accompanying balance sheet reflects the fair value of
the trading asset or $621,000 in other current assets and the fair value of the
trading liability or $863,000 in accrued liabilities.





                                      -10-

<PAGE>   11

                           PART II. OTHER INFORMATION

Item 1. - None

Item 2. - None

Item 3. - None

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

         The 1999 Annual Meeting of Stockholders (the "Meeting") of the Company
was held on April 28, 1999. At the Meeting, holders of common stock, $.10 par
value, of the Company elected nine members of the Company's Board of Directors.

         Out of the 4,217,596 shares of common stock entitled to vote at the
Meeting, there were 3,922,364 shares of common stock voted for the election of
the nominees for Directors listed in the proxy statement.

Item 6.  Exhibits and Reports on Form 8K  

      a.    Exhibits - None.
      b.    Reports on Form 8-K - None.



                                      -11-



<PAGE>   12







         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: May 13, 1999                      By  /s/ K. S. Adams, Jr.
     ----------------                      -------------------------------------
                                            K. S. Adams, Jr.
                                            Chief Executive Officer



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


                                      -12-

<PAGE>   13

                                  EXHIBIT INDEX

<TABLE>
<CAPTION>

Exhibit
Number          Description             
-------         -----------

<S>             <C>                          
27*      -      Financial Data Schedule
</TABLE>



------------------------------
*  - Filed herewith




                                      -13-