<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

[X]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934 - FOR THE QUARTERLY PERIOD ENDED MARCH 31, 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:    0-22276

                              ALLIED HOLDINGS, INC.
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

             GEORGIA                                    58-0360550
--------------------------------------------------------------------------------
(State or other jurisdiction of                      (I.R.S. Employer
 incorporation or organization)                    Identification Number)

            SUITE 200, 160 CLAIREMONT AVENUE, DECATUR, GEORGIA 30030
--------------------------------------------------------------------------------
                    (Address of principal executive offices)

                                 (404) 373-4285
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)


--------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)

         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. [X] Yes [ ] No


<TABLE>
<S>                                                                    <C>
Outstanding common stock, No par value at May 1, 1998................. 7,877,547
</TABLE>




                TOTAL NUMBER OF PAGES INCLUDED IN THIS REPORT: 11


                                       1
<PAGE>   2
                                      INDEX

                                     PART I

                              FINANCIAL INFORMATION

<TABLE>
<CAPTION>
                                                                                PAGE
<S>      <C>                                                                    <C>
ITEM 1:           FINANCIAL STATEMENTS
-------           --------------------

         Consolidated Balance Sheets as of  March 31, 1998 and
          December 31,  1997....................................................  3

         Consolidated Statements of Operations for the Three
          Month Periods Ended March 31, 1998 and 1997...........................  4

         Consolidated Statements of Cash Flows for the Three
          Month Periods Ended March 31, 1998 and 1997...........................  5

         Notes to Consolidated Financial Statements.............................  6


ITEM 2
------
         Management's Discussion and Analysis of Financial
          Condition  and Results of  Operations.................................  8



                                     PART II

                                OTHER INFORMATION

ITEM 6
------

         Exhibits and Reports on Form 8-K....................................... 10

         Signature Page......................................................... 11
</TABLE>




                                       2
<PAGE>   3
PART 1 - FINANCIAL INFORMATION
ITEM 1 - FINANCIAL STATEMENTS

                     ALLIED HOLDINGS, INC. AND SUBSIDIARIES

                           CONSOLIDATED BALANCE SHEETS
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                           MARCH 31      DECEMBER 31
                                                                             1998            1997
                                                                         -----------     -----------
                                                                         (UNAUDITED)
<S>                                                                      <C>             <C>
                                     ASSETS

CURRENT ASSETS:
         Cash and cash equivalents                                        $   4,452       $  10,530
         Short-term investments                                              22,255          19,540
         Receivables, net of allowance for doubtful accounts                 86,986          74,881
         Inventories                                                          5,977           5,391
         Deferred tax assets                                                 17,837          17,812
         Prepayments and other current assets                                23,493          21,519
                                                                          ---------       ---------
                  Total current assets                                      161,000         149,673
                                                                          ---------       ---------

PROPERTY AND EQUIPMENT, NET                                                 280,763         286,214
                                                                          ---------       ---------

OTHER ASSETS:
         Goodwill, net                                                       98,911          99,310
         Notes receivable due from related parties                                0             573
         Other                                                               35,990          23,169
                                                                          ---------       ---------
                  Total other assets                                        134,901         123,052
                                                                          ---------       ---------
                  Total assets                                            $ 576,664       $ 558,939
                                                                          =========       =========

         LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES:
         Current maturities of long-term debt                             $   2,986       $   2,980
         Trade accounts payable                                              33,882          36,263
         Accrued liabilities                                                120,579         118,436
                                                                          ---------       ---------
                  Total current liabilities                                 157,447         157,679
                                                                          ---------       ---------

LONG-TERM DEBT, LESS CURRENT MATURITIES                                     246,272         228,003
                                                                          ---------       ---------

POSTRETIREMENT BENEFITS OTHER THAN PENSIONS                                  11,321          11,355
                                                                          ---------       ---------

DEFERRED INCOME TAXES                                                        35,348          35,062
                                                                          ---------       ---------

OTHER LONG-TERM LIABILITIES                                                  67,824          69,512
                                                                          ---------       ---------

STOCKHOLDERS' EQUITY:
         Common stock, no par value; 20,000 shares authorized, 7,878
                  and 7,819 shares outstanding at March 31, 1998
                  and December 31,1997, respectively                              0               0
         Additional paid-in capital                                          44,806          43,758
         Retained earnings                                                   17,569          16,877
         Foreign currency translation adjustment, net of tax                 (2,439)         (2,826)
         Unearned compensation                                               (1,484)           (481)
                                                                          ---------       ---------
                  Total stockholders' equity                                 58,452          57,328
                                                                          ---------       ---------
                  Total liabilities and stockholders' equity              $ 576,664       $ 558,939
                                                                          =========       =========
</TABLE>

              The accompanying notes are an integral part of these
                          consolidated balance sheets.


                                       3
<PAGE>   4
                     ALLIED HOLDINGS, INC. AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF OPERATIONS
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)
                                   (UNAUDITED)



<TABLE>
<CAPTION>
                                                     FOR THE THREE MONTHS ENDED
                                                              MARCH 31
                                                     --------------------------
                                                        1998             1997
                                                        ----             ----
<S>                                                  <C>              <C>      
REVENUES                                             $ 253,390        $  96,393
                                                     ---------        ---------

OPERATING EXPENSES:
     Salaries, wages and fringe benefits               143,976           51,942
     Operating supplies and expenses                    44,626           15,256
     Purchased transportation                           20,814            8,950
     Insurance and claims                                9,133            3,809
     Operating taxes and licenses                        8,663            3,858
     Depreciation and amortization                      12,925            6,847
     Rents                                               3,029            1,231
     Communications and utilities                        1,913              770
     Other operating expenses                            1,524              924
                                                     ---------        ---------
         Total operating expenses                      246,603           93,587
                                                     ---------        ---------
         Operating income                                6,787            2,806
                                                     ---------        ---------

OTHER INCOME (EXPENSE):
     Interest expense                                   (6,022)          (2,616)
     Interest income                                       456              152
                                                     ---------        ---------
                                                        (5,566)          (2,464)
                                                     ---------        ---------

INCOME BEFORE INCOME TAXES                               1,221              342

INCOME TAX PROVISION                                      (531)            (144)
                                                     ---------        ---------

NET INCOME                                           $     690        $     198
                                                     =========        =========


NET INCOME PER COMMON SHARE-BASIC
AND DILUTED                                          $    0.09        $    0.03
                                                     =========        =========

WEIGHTED AVERAGE COMMON
SHARES OUTSTANDING                                       7,746            7,725
                                                     =========        =========
</TABLE>

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


                                        4
<PAGE>   5
                     ALLIED HOLDINGS, INC. AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                            FOR THE THREE MONTHS ENDED
                                                                                      MARCH 31
                                                                            --------------------------
                                                                                1998           1997
                                                                            -----------    -----------
<S>                                                                         <C>            <C>     
CASH FLOWS FROM OPERATING ACTIVITIES:
       Net income                                                             $    690       $    198
                                                                              --------       --------
       Adjustments to reconcile net income to net cash used in operating
         activities:
            Depreciation and amortization                                       12,925          6,847
            Loss (gain) on sale of property and equipment                           37             (4)
            Deferred income taxes                                                   76           (505)
            Change in operating assets and liabilities:
                 Receivables, net of allowance for doubtful accounts           (11,973)        (6,233)
                 Inventories                                                      (574)           448
                 Prepayments and other current assets                           (1,949)        (2,472)
                 Trade accounts payable                                         (2,431)        (2,887)
                 Accrued liabilities                                               360          3,811
                                                                              --------       --------
                    Total adjustments                                           (3,529)          (995)
                                                                              --------       --------
                    Net cash used in operating activities                       (2,839)          (797)
                                                                              --------       --------


CASH FLOWS FROM INVESTING ACTIVITIES:
       Purchases of property and equipment                                      (6,396)        (3,850)
       Proceeds from sale of property and equipment                                115              8
       Investment in joint venture                                             (11,920)             0
       Increase in short-term investments                                       (2,715)        (2,004)
       Increase in the cash surrender value of life insurance                     (620)          (667)
                                                                              --------       --------
                    Net cash used in investing activities                      (21,536)        (6,513)
                                                                              --------       --------


CASH FLOWS FROM FINANCING ACTIVITIES:
       Proceeds from issuance of long-term debt                                 18,269          7,986
       Other, net                                                                   94            117
                                                                              --------       --------
                    Net cash provided by financing activities                   18,363          8,103
                                                                              --------       --------


EFFECT OF EXCHANGE RATE CHANGES ON CASH
       AND CASH EQUIVALENTS                                                        (66)           (81)


NET (DECREASE) INCREASE IN CASH AND CASH EQUIVALENTS                            (6,078)           712


CASH AND CASH EQUIVALENTS AT BEGINNING OF YEAR                                  10,530          1,973
                                                                              --------       --------


CASH AND CASH EQUIVALENTS AT END OF PERIOD                                    $  4,452       $  2,685
                                                                              ========       ========
</TABLE>



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


                                        5
<PAGE>   6
                     ALLIED HOLDINGS, INC. AND SUBSIDIARIES
             Notes to Consolidated Financial Statements (Unaudited)


Note 1.  Basis of Presentation

         The unaudited consolidated financial statements included herein have
         been prepared pursuant to the rules and regulations of the Securities
         and Exchange Commission. Accordingly, they do not include all of the
         information and footnotes required by generally accepted accounting
         principles for complete financial statements. The statements contained
         herein reflect all adjustments, all of which are of a normal, recurring
         nature, which are, in the opinion of management, necessary to present
         fairly the financial condition, results of operations and cash flows
         for the periods presented. Operating results for the three month period
         ended March 31, 1998 are not necessarily indicative of the results that
         may be expected for the year ended December 31, 1998. The interim
         financial statements should be read in conjunction with the financial
         statements and notes thereto of Allied Holdings, Inc. and Subsidiaries,
         (the "Company") included in the Company's 1997 Annual Report on Form
         10-K.

Note 2.  Long-Term Debt

         On September 30, 1997, the Company issued $150 million of 8 5/8% senior
         notes (the "Notes") through a private placement. Subsequently, the
         Notes were registered with the Securities and Exchange Commission. The 
         net proceeds from the Notes were used to fund the acquisition of Ryder
         Automotive Carrier Services, Inc. and RC Management Corp., pay related
         fees and expenses, and reduce outstanding indebtedness. The Company's
         obligations under the Notes are guaranteed by substantially all of the
         subsidiaries of the Company (the "Guarantors"). Separate financial
         statements of the Guarantors are not provided herein as (i) the
         Guarantors are jointly and severally liable for the Company's
         obligations under the Notes, (ii) the subsidiaries which are not
         Guarantors are inconsequential to the consolidated operations of the
         Company and its subsidiaries and (iii) the net assets and earnings of
         the Guarantors are substantially equivalent to the net assets and
         earnings of the consolidated entity as reflected in these consolidated
         financial statements. There are no restrictions on the ability of the
         Guarantors to make distributions to the Company.

Note 3.  Acquisition of Ryder Automotive Carrier Services, Inc. and RC 
         Management Corp.

         On September 30, 1997, the Company completed the acquisition of Ryder
         Automotive Carrier Services, Inc. and RC Management Corp. from Ryder
         System, Inc. for approximately $114.5 million in cash, subject to
         post-closing adjustments. The subsidiaries of Ryder Automotive Carrier
         Inc. Services are engaged in car hauling, vehicle processing and dealer
         prep, rail unloading and loading services of vehicle railcars, and rail
         and port yard management. RC Management Corp. is principally involved
         in providing logistics services to the new retail used car superstores.
         The operating results of Ryder's Automotive Carrier Group have been
         included with the Company's since the date of the acquisition.


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<PAGE>   7

Note 4.  Investment in Axis do Brasil

         In February of 1998, the Company's wholly owned subsidiary, Axis Group,
         Inc. completed the formation of a 50 percent owned venture in Brazil.
         The Brazilian venture, Axis do Brasil, is a partnership with Coimex
         Trading Company of Vitoria, Brazil, which is one of the largest trading
         companies in South America. Axis do Brasil is an equity partner in a
         newly formed Brazilian firm, Axis Sinimbu Logistica ("ASL"). ASL will
         provide supply chain logistics services for the automotive industry in
         the Mercosur counties.

Note 5.  Comprehensive Income

         Comprehensive income was $1.1 million for the first quarter of 1998
         versus a Loss of $0.1 million for the first quarter of 1997.  The
         difference between comprehensive income and net income is the foreign
         currency translation adjustment, net of income taxes.

Note 6.  Earnings per Share

         In February 1997, the Financial Accounting Standards Board issued SFAS
         No. 128, "Earnings per Share." This new statement did not result in
         changes to the Company's earnings per share for the first quarters of 
         1997.










                                        7
<PAGE>   8
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

RESULTS OF OPERATIONS

         Revenues were $253.4 million for the first quarter of 1998 versus
         revenues of $96.4 million for the first quarter of 1997, an increase of
         163%. Net income was $0.7 million in the first quarter of 1998 versus
         $0.2 million in the first quarter of 1997, or $0.09 per diluted share
         in 1998, versus $0.03 per diluted share in 1997, an increase of 248 %.
         The significant increase in the Company's revenues was primarily due to
         the acquisition of Ryder's Automotive Carrier Group which was completed
         on September 30, 1997. The operating results of Ryder's Automotive
         Carrier Group have been included with Allied's since the date of the
         acquisition. The combined companies had a 5 % increase in vehicles
         delivered for the first quarter of 1998 versus 1997 which led to the
         significant increase in net income. The increase in vehicle deliveries
         was primarily due to increases in new vehicle production together with
         an increase in off-rail deliveries due to rail-car shortages.

         Salaries, wages and fringe benefits increased from 53.9 % of revenues
         in the first quarter of 1997 to 56.8 % for the first quarter of 1998.
         The increase was primarily due to annual salary and benefit increases
         offset by continued productivity and efficiency improvements. In
         addition, there has been an increase in the number of vehicles
         delivered by company drivers versus owner-operators during the first
         quarter of 1998 versus 1997. This results in an increase in salaries,
         wages and fringe benefits and operating supplies and expenses and a
         decrease in purchased transportation.  Owner-operators are responsible
         for all costs to operate their rigs and such costs are included in
         purchased transporation.

         Operating supplies and expenses increased from 15.8 % of revenues in
         the first quarter of 1997 to 17.6 % for the first quarter of 1998. The
         increase was primarily the result of the acquisition of Ryder
         Automotive Carrier Group as its operating costs as a percentage of
         revenues were higher than the Company's together with an increase in
         the vehicles delivered by Company drivers versus owner operators.

         Purchased transportation expense decreased from 9.3 % of revenues in
         the first quarter of 1997 to 8.2 % for the first quarter of 1998. The
         decrease was primarily due to the decrease in the mix of 
         owner-operators to Company drivers and the ability to haul more 
         vehicles with Company drivers thus reducing the number of vehicles 
         delivered by other carriers for the Company. All costs for 
         owner-operators are included in purchased transportation.

         Insurance and claims expense decreased from 4.0 % of revenues in the
         first quarter of 1997 to 3.6 % for the first quarter of 1998. The
         decrease was primarily due to lower cargo claims costs resulting from
         the continuation of quality programs instituted in 1997.

         Depreciation and amortization expense decreased from 7.1 % of revenues
         in the first quarter of 1997 to 5.1 % for the first quarter of 1998.
         The decrease was primarily the result of depreciation expense on the
         rigs acquired through the acquisition of Ryder Automotive Carrier Group
         representing a lower percentage of revenues than the Company's due to
         the age and useful lives of the rigs.




                                       8
<PAGE>   9
FINANCIAL CONDITION, LIQUIDITY AND CAPITAL RESOURCES


         Net cash used by operating activities totaled $0.8 million in the first
         quarter of 1997 versus $2.8 million for the first quarter of 1998. The
         increase in cash used by operating activities was primarily due to
         seasonal working capital increases due to the seasonality of the
         Company's revenues.

         Net cash used in investing activities totaled $6.5 million in the first
         quarter of 1997 versus $21.5 million for the first quarter of 1998. The
         increase was primarily due to the investment of $11.9 million in Axis
         do Brasil in February 1998. Capital expenditures increased from $3.9
         million in the first quarter of 1997 to $6.4 million for the first
         quarter of 1998. The increase in capital expenditures was due to the
         increase in the number of new tractors and trailers purchased by the
         Company together with an increase in modifications to existing
         tractors and trailers due to an increase in the fleet size as a result
         of the Ryder Automotive Carrier Group acquisition.

         Net cash provided by financing activities totaled $8.1 million versus
         $18.4 million for the first quarter of 1997 versus 1998. The increase
         was primarily due to borrowings to finance the Company's investment in
         Axis do Brasil.



         SEASONALITY AND INFLATION

         The Company's revenues are seasonable, with the second and fourth
         quarters generally experiencing higher revenues than the first and
         third quarters. The volume of vehicles shipped during the second and
         fourth quarters is generally higher due to the introduction of new
         models which are shipped to dealers during those periods and the higher
         spring and early summer sales of automobiles and light trucks. During
         the first and third quarters, vehicle shipments typically decline due
         to lower sales volume during those periods and scheduled plant shut
         downs. Inflation has not significantly affected the Company's results
         of operations.




                                       9
<PAGE>   10
                                     PART II


                                OTHER INFORMATION


ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K.

         (a)      Exhibits: 
                  
         27       Financial Data Schedule (for SEC use only)

         (b)      Reports on Form 8-K: There were no reports filed on Form 8-K
                                       for the quarter ended March 31, 1998.










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<PAGE>   11
                                   SIGNATURES


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.

                                             Allied Holdings, Inc.



March 13, 1998                               /s/A. Mitchell Poole, Jr.
--------------                               -------------------------
    (Date)                                   A. Mitchell Poole, Jr.
                                             on behalf of Registrant as
                                             President, Chief Operating Officer,
                                             Chief Financial Officer and
                                             Assistant Secretary











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