<PAGE>   1
===============================================================================
                       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 PERIOD ENDED MAY 29, 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 33-68412
                                ---------------

                             AVONDALE INCORPORATED
             (Exact name of registrant as specified in its charter)


                 GEORGIA                                  58-0477150
   (State or other jurisdiction of                     (I.R.S. employer
     incorporation or organization)                    identification no.)

      506 SOUTH BROAD STREET                                30655
           MONROE, GEORGIA                                (Zip code)
   (Address of principal executive
               offices)


       Registrant's telephone number, including area code: (770) 267-2226


   Former name, former address and former fiscal year, if changed since last
                                  report: N/A


       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 
                                              ---    ---

       Indicate the number of shares outstanding of each of the issuer's
classes of common stock, as of the latest practicable date.

<TABLE>
<CAPTION>
        Description                   As Of             Shares Outstanding
   --------------------           ------------          ------------------
   <S>                            <C>                   <C>
   Class A Common Stock           July 6, 1998          11,698,184 Shares
   Class B Common Stock           July 6, 1998             978,939 Shares
</TABLE>


===============================================================================
<PAGE>   2


                                   FORM 10-Q

                               TABLE OF CONTENTS


<TABLE>
<CAPTION>
PART  I  -  FINANCIAL INFORMATION  (UNAUDITED)

        <S>         <C>                                                                                           <C>
        Item 1:     Financial Statements

                    Condensed Consolidated Balance Sheets at May 29, 1998 and August 29, 1997..................   1

                    Condensed Consolidated Statements of Income for the Thirteen Weeks Ended
                    May 29, 1998 and May 30, 1997..............................................................   2

                    Condensed Consolidated Statements of Income for the  Thirty-Nine
                    Weeks Ended May 29, 1998 and May 30, 1997..................................................   3

                    Condensed Consolidated Statements of Shareholders' Equity for the
                    Thirty-Nine Weeks Ended May 29, 1998 and May 30, 1997......................................   4

                    Condensed Consolidated Statements of Cash Flows for the Thirty-Nine Weeks
                    Ended May 29, 1998 and May 30, 1997........................................................   5

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

        Item 2:     Management's Discussion and Analysis of Financial Condition and Results of 
                    Operations.................................................................................   9

        Item 3:     Quantitative and Qualitative Disclosures about Market Risk.................................  12

PART  II - OTHER INFORMATION


        Item 1:     Legal Proceedings..........................................................................  13

        Item 2:     Changes in Securities and Use of Proceeds..................................................  13

        Item 3:     Defaults upon Senior Securities............................................................  13

        Item 4:     Submission of Matters to a Vote of Security Holders........................................  13

        Item 5:     Other Information..........................................................................  13

        Item 6:     Exhibits and Reports on Form 8-K...........................................................  13

        Signature..............................................................................................  14
</TABLE>

<PAGE>   3

PART I - FINANCIAL INFORMATION
ITEM 1.  FINANCIAL STATEMENTS

                             AVONDALE INCORPORATED
               CONDENSED CONSOLIDATED BALANCE SHEETS (UNAUDITED)
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)

<TABLE>
<CAPTION>

                                                                                    AUG. 29,            MAY 29,
                                                                                      1997                1998
                                                                                  ------------         ---------
                                                       ASSETS
<S>                                                                               <C>                  <C>
Current assets
   Cash                                                                           $      8,517         $   3,135
   Accounts receivable, less allowance for doubtful accounts
      of $5,518 in 1997 and $3,283 in 1998                                              77,698            65,264
   Inventories                                                                         120,860           147,295
   Prepaid expenses                                                                      1,561             1,264
                                                                                  ------------         ---------

      Total current assets                                                             208,636           216,958
Property, plant and equipment
   Land                                                                                  8,510             8,510
   Buildings                                                                            71,155            78,894
   Machinery and equipment                                                             379,434           415,766
                                                                                  ------------         ---------
                                                                                       459,099           503,170
   Less accumulated depreciation                                                      (230,117)         (258,732)
                                                                                  ------------         ---------

                                                                                       228,982           244,438

Other assets                                                                            23,604            22,349
                                                                                  ------------         ---------


                                                                                  $    461,222         $ 483,745
                                                                                  ============         =========

                                        LIABILITIES AND SHAREHOLDERS' EQUITY
Current liabilities
   Accounts payable                                                               $     41,884         $  41,110
   Accrued compensation, benefits and related expenses                                  22,514            26,335
   Other accrued expenses                                                               22,416            17,818
   Long-term debt due in one year                                                        3,250             3,250
   Income taxes payable                                                                  4,804             2,087
                                                                                  ------------         ---------
      Total current liabilities                                                         94,868            90,600

Long-term debt                                                                         248,075           268,525
Deferred income taxes and other long-term liabilities                                   31,917            34,700
Shareholders' equity
  Preferred stock
        $.01 par value; 10,000 shares authorized                                            --                --
  Common stock
        Class A, $.01 par value; 100,000 shares
            authorized; issued and outstanding - 12,290 shares in 1997
            and 11,698 shares in 1998                                                      123               117
        Class B, $.01 par value; 5,000 shares authorized; issued and
            outstanding - 979 shares in 1997 and 1998                                       10                10
  Capital in excess of par value                                                        41,478            39,837
  Retained earnings                                                                     44,751            49,956
                                                                                  ------------         ---------
      Total shareholders' equity                                                        86,362            89,920
                                                                                  ------------         ---------

                                                                                  $    461,222         $ 483,745
                                                                                  ============         =========
</TABLE>


           See notes to condensed consolidated financial statements.



                                       1
<PAGE>   4

                             AVONDALE INCORPORATED
            CONDENSED CONSOLIDATED STATEMENTS OF INCOME (UNAUDITED)
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)


<TABLE>
<CAPTION>

                                                                  THIRTEEN WEEKS ENDED
                                                             -----------------------------
                                                                MAY 30,           MAY 29,
                                                                 1997              1998
                                                             -----------        ----------

<S>                                                          <C>                <C>
Net sales                                                    $   277,182        $  271,286

Operating costs and expenses
  Cost of goods sold                                             229,230           225,649
  Depreciation                                                     9,947             9,848
  Selling and administrative expenses                             11,298            13,047
  Facility restructuring                                              --             2,699
                                                             -----------        ----------
      Operating income                                            26,707            20,043

Interest expense                                                   6,682             6,111
Discount and expenses on sale of receivables                       1,559             1,688
Loss attributable to investment in Oneita                          1,300                --
Other income, net                                                    (59)              (10)
                                                             -----------        ----------

  Income before income taxes                                      17,225            12,254

Provision for income taxes                                         6,930             4,420
                                                             -----------        ----------

      Net income                                             $    10,295        $    7,834
                                                             ===========        ==========

Per share data:
      Net income - basic                                     $       ,77        $      ,60
                                                             ===========        ==========

      Net income- diluted                                    $       ,77        $      ,59
                                                             ===========        ==========

      Dividends declared                                     $       ,07        $      ,10
                                                             ===========        ==========
</TABLE>



           See notes to condensed consolidated financial statements.



                                       2
<PAGE>   5


                             AVONDALE INCORPORATED
            CONDENSED CONSOLIDATED STATEMENTS OF INCOME (UNAUDITED)
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)

<TABLE>
<CAPTION>

                                                              THIRTY-NINE WEEKS ENDED
                                                        ----------------------------------
                                                           MAY 30,               MAY 29,
                                                            1997                  1998
                                                        ------------           -----------

<S>                                                     <C>                    <C>
Net sales                                               $    778,876           $   790,352

Operating costs and expenses
  Cost of goods sold                                         662,761               661,740
  Depreciation                                                30,508                29,511
  Selling and administrative expenses                         33,914                35,774
  Facility restructuring                                          --                 2,699
                                                        ------------           -----------
      Operating income                                        51,693                60,628

Interest expense                                              20,095                17,482
Discount and expenses on sale of receivables                   4,795                 5,534
Loss attributable to investment in Oneita                      6,456                    --
Other expense, net                                               370                   213
                                                        ------------           -----------

  Income before income taxes                                  19,977                37,399

Provision for income taxes                                     8,040                14,480
                                                        ------------           -----------

      Net income                                        $     11,937           $    22,919
                                                        ============           ===========

Per share data:
      Net income - basic                                $        ,90           $      1.73
                                                        ============           ===========

      Net income - diluted                              $        ,89           $      1.71
                                                        ============           ===========

      Dividends declared                                $        ,21           $       ,30
                                                        ============           ===========
</TABLE>


           See notes to condensed consolidated financial statements.



                                       3
<PAGE>   6


                             AVONDALE INCORPORATED
           CONDENSED CONSOLIDATED STATEMENTS OF SHAREHOLDERS' EQUITY
                                  (UNAUDITED)
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)


<TABLE>
<CAPTION>
                                                                    
                                                               COMMON STOCK                    
                                                                   ISSUED          CAPITAL IN
                                                          -----------------------  EXCESS OF     RETAINED
                                                             SHARES      AMOUNT    PAR VALUE     EARNINGS
                                                          -----------  ----------  ---------    ----------
<S>                                                       <C>          <C>         <C>          <C>
Balance at August 30, 1996........................             13,291  $      133  $  41,844    $   25,535
  Net income......................................                 --          --         --        11,937
  Cash dividends ($0.21 per share)................                 --          --        --         (2,791)
                                                          -----------  ----------  ---------    ----------
Balance at May 30, 1997...........................             13,291  $      133  $  41,844    $   34,681
                                                          ===========  ==========  =========    ==========
                                                                             




Balance at August 29, 1997........................             13,269  $      133  $  41,478    $   44,751
  Net income......................................                 --          --         --        22,919
  Cash dividends ($0.30 per share)................                 --          --         --        (3,981)
  Purchase and retirement of treasury stock.......               (592)         (6)    (1,641)      (13,733)
                                                          -----------  ----------  ---------    ----------
Balance at May 29, 1998...........................             12,677  $      127  $  39,837    $   49,956
                                                          ===========  ==========  =========    ==========
</TABLE>


           See notes to condensed consolidated financial statements.



                                       4

<PAGE>   7
                             AVONDALE INCORPORATED
          CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS (UNAUDITED)
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>

                                                                                  THIRTY-NINE WEEKS ENDED
                                                                                ----------------------------
                                                                                  MAY 30,            MAY 29,
                                                                                   1997               1998
                                                                                ---------           --------
<S>                                                                             <C>                 <C>
Operating activities
   Net income                                                                   $ 11,937            $ 22,919
   Adjustments to reconcile net income to net
       cash provided by operating activities:
         Depreciation and amortization                                            30,730              29,805
         Loss attributable to investment in Oneita                                 6,456                  --
         Facility restructuring                                                       --               2,699
         Provision for deferred income taxes                                       3,696               1,530
         (Gain) loss on sale of equipment                                             (5)                305
         Changes in operating assets and liabilities                             (13,057)            (25,620)
                                                                                --------            --------

             Net cash provided by operating activities                            39,757              31,638
                                                                                --------            --------

Investing activities
   Due from TRIARC                                                                 7,250                  --
   Purchases of property, plant and equipment                                    (17,766)            (47,152)
   Proceeds from sale of property, plant and equipment                             1,172                  43
                                                                                --------            --------

             Net cash used in investing activities                                (9,344)            (47,109)
                                                                                --------            --------

Financing activities
   Net borrowings (payments) on revolving line of credit
       and long term debt                                                        (36,925)             20,450
   Sale of accounts receivable                                                    10,000               9,000
   Purchase and retirement of treasury stock                                          --             (15,380)
   Dividends paid                                                                 (2,791)             (3,981)
                                                                                --------            --------

              Net cash provided by (used in) financing activities                (29,716)             10,089
                                                                                --------            --------

Increase (decrease) in cash                                                          697              (5,382)

Cash at beginning of period                                                        7,253               8,517
                                                                                --------            --------

              Cash at end of period                                             $  7,950            $  3,135
                                                                                ========            ========
</TABLE>


           See notes to condensed consolidated financial statements.



                                       5
<PAGE>   8
                                        
                             AVONDALE INCORPORATED
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                  (UNAUDITED)
                                  MAY 29, 1998
                                        


         1. Basis of Presentation: The accompanying unaudited condensed
consolidated financial statements include the accounts of Avondale Incorporated
and its wholly owned subsidiaries, Avondale Mills, Inc. and Avondale
Receivables Company (collectively, the "Company"). These statements have been
prepared in accordance with generally accepted accounting principles for
interim financial information. Accordingly, they do not include all of the
information and footnotes required by generally accepted accounting principles
for complete financial statements. The August 29, 1997 balance sheet has been
derived from the audited financial statements at that date. The accounting
policies and basis of presentation followed by the Company are presented in
Note 1 to the August 29, 1997 Audited Consolidated Financial Statements.

         The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period. Actual results could differ from those estimates.

         In the opinion of management, the accompanying unaudited condensed
consolidated financial statements contain all adjustments (consisting of normal
recurring accruals) necessary for a fair presentation. Operating results for
the thirty-nine weeks ended May 29, 1998 are not necessarily indicative of the
results that may be expected for the fiscal year ending August 28, 1998.

         2. Inventories: Components of inventories are as follows (amounts in
thousands):

<TABLE>
<CAPTION>
                                                                               AUG. 29,       MAY 29,
                                                                                1997           1998
                                                                              ---------      ---------
         <S>                                                                  <C>            <C>
         Finished goods                                                       $  32,907         42,784
         Work in process                                                         51,345         63,846
         Raw materials                                                           24,556         27,728
         Dyes and chemicals                                                       6,518          6,427
                                                                              ---------      ---------
         Inventories at FIFO                                                    115,326        140,785

         Less allowance to reduce carrying value to
            LIFO basis                                                           (2,027)          (977)
                                                                              ---------      ---------
                                                                                113,299        139,808
         Supplies at average cost                                                 7,561          7,487
                                                                              ---------      ---------

                                                                              $ 120,860      $ 147,295
                                                                              =========      =========
</TABLE>



                                       6
<PAGE>   9


                             AVONDALE INCORPORATED
          NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (CONT.)
                                  (UNAUDITED)
                                  MAY 29, 1998


         Valuation of the Company's inventories under the last-in, first-out
(LIFO) method at May 29, 1998 and the related impact on the statement of income
for the thirty-nine weeks then ended has been determined using estimated
quantities and costs as of the fiscal 1998 year-end. As a result, interim
amounts are subject to the final year-end LIFO valuation.

         3. Earnings Per Share: Effective May 29, 1998, the Company adopted
Statement of Financial Accounting Standards No. 128, "Earnings Per Share." In
accordance with Statement 128, basic and diluted earnings per share are
reported for all periods presented, replacing the previously reported primary
and fully diluted earnings per share. Unlike primary earnings per share, basic
earnings per share excludes any dilutive effects of stock options and similar
items. Diluted earnings per share is very similar to the previously reported
fully diluted earnings per share.

         Earnings per share is calculated by dividing the reported net income
for the period by the appropriate weighted average number of shares of common
stock outstanding, as shown below (amounts in thousands):


<TABLE>
<CAPTION>
                                                        THIRTEEN WEEKS ENDED               THIRTY-NINE WEEKS ENDED
                                                     --------------------------         -----------------------------
                                                       MAY 30,         MAY 29,            MAY 30,            MAY 29,
                                                        1997            1998               1997               1998
                                                     ----------       ---------         -----------        ----------
          <S>                                        <C>              <C>               <C>                <C>
          Weighted average shares outstanding -
               basic                                     13,291          13,145              13,291            13,228
          Effect of employee stock options                  109             224                 109               194
                                                     ----------       ---------         -----------        ----------
          Weighed average shares outstanding- 
               diluted                                   13,400          13,369              13,400            13,422
                                                     ==========       =========         ===========        ==========
</TABLE>


         4. Facility Restructuring: During the third quarter of fiscal 1998,
the Company recorded pretax charges of $2.7 million to consolidate
manufacturing facilities and dispose of certain inefficient equipment in its
Graniteville, South Carolina operations.

         5. Common Stock: On May 10, 1998, the Company repurchased 592,000
shares of Class A Common Stock for an aggregate purchase price of $15.4
million. These shares were repurchased pursuant to a tender offer, distributed
to all shareholders and vested stock option holders of the Company's Class A
Common Stock, to purchase for cash up to $18.0 million worth of Class A Common
Stock. All shares repurchased have been canceled and reinstated as authorized
but unissued shares of Class A Common Stock.

         In conjunction with the stock repurchase described above, certain
participants in the Company's Stock Option Plan redeemed options in exchange
for an aggregate cash payment of $1.2 million. The redemption included 85,000
options to acquire shares of Class A Common Stock at $12.50 per share and
10,000 options to acquire shares of Class A Common Stock at $18.00 per share.
The Company recorded the cost of the redemption as compensation expense, which
is included in selling and administrative expenses. After the redemption, there
were 850,000 stock options outstanding, 401,000 of which were exercisable.



                                       7
<PAGE>   10

                             AVONDALE INCORPORATED
          NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (CONT.)
                                  (UNAUDITED)
                                  MAY 29, 1998

      6. Contingencies: The Company is involved in certain environmental
matters and claims. The Company has provided reserves to cover management's
estimates of the cost of investigating, monitoring and remediating these and
other environmental conditions. If more costly remediation measures are
necessary than those believed to be probable based on current facts and
circumstances, actual costs may exceed the reserves provided. However, based on
the information currently available, management does not believe that the
outcome of these matters will have a material adverse effect on its future
results of operations or financial position.

         The Company is also a party to litigation incidental to its business
from time to time. The Company is not currently a party to any litigation that
management, in consultation with legal counsel, believes, if determined
adversely to the Company, would have a material adverse effect on the Company's
financial condition or results of operations.



                                       8
<PAGE>   11

ITEM 2:   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
          RESULTS OF OPERATIONS

RESULTS OF OPERATIONS

Thirteen Weeks Ended May 29, 1998  Compared to Thirteen Weeks Ended May 30, 
1997

         NET SALES. Net sales decreased 2.1% to $271.3 million for the thirteen
weeks ended May 29, 1998 from $277.2 million for the thirteen weeks ended May
30, 1997, primarily as a result of declining apparel fabric sales.

         Apparel fabric sales decreased 2.8% to $183.7 million for the thirteen
weeks ended May 29, 1998 from $189.0 million for the thirteen weeks ended May
30, 1997, reflecting a 3.5% decline in average selling prices. This decline in
average selling prices resulted from softening market prices caused by excess
inventories of fabrics and garments within the industry, as well as increased
production capacity of domestic and international suppliers.

         Greige and specialty fabric sales decreased 0.6% to $18.1 million for
the thirteen weeks ended May 29, 1998 from $18.2 million for the thirteen weeks
ended May 30, 1997.

         Yarn sales decreased 0.7% to $69.5 million for the thirteen weeks
ended May 29, 1998 from $70.0 million for the thirteen weeks ended May 30,
1997. This decrease reflected a 1.2% increase in pounds sold and a 1.9%
decrease in average selling prices for those pounds. Market prices for sales
yarns remained very competitive, reflecting continued excess production
capacity within the industry during the thirteen weeks ended May 29, 1998.

         COST OF GOODS SOLD. Cost of goods sold decreased 1.6% to $225.6
million for the thirteen weeks ended May 29, 1998 from $229.2 million for the
thirteen weeks ended May 30, 1997. Cost of goods sold as a percentage of net
sales increased to 83.2% for the thirteen weeks ended May 29, 1998 from 82.7%
for the thirteen weeks ended May 30, 1997, primarily due to the impact of lower
average selling prices.

         SELLING AND ADMINISTRATIVE EXPENSES. Selling and administrative
expenses increased 15.5% to $13.0 million for the thirteen weeks ended May 29,
1998 from $11.3 million for the thirteen weeks ended May 30, 1997, reflecting
increased accrual of certain associate benefit expenses and compensation
expense related to the redemption of stock options by certain current and
former associates of the Company. Selling and administrative expenses as a
percentage of net sales increased to 4.8% for the thirteen weeks ended May 29,
1998 from 4.1% for the thirteen weeks ended May 30, 1997.

         FACILITY RESTRUCTURING. Charges incurred to consolidate manufacturing
facilities and dispose of certain inefficient equipment in the Company's
Graniteville, South Carolina operations were $2.7 million for the thirteen
weeks ended May 29, 1998.

         INTEREST EXPENSE, NET. Interest expense, net decreased 8.6% to $6.1
million for the thirteen weeks ended May 29, 1998 from $6.7 million for the
thirteen weeks ended May 30, 1997. This decrease reflected lower interest rates
and a lower average balance of outstanding borrowings during the thirteen weeks
ended May 29, 1998.

         DISCOUNT AND EXPENSES ON SALE OF RECEIVABLES. Discount and expenses on
sale of receivables were $1.7 million for the thirteen weeks ended May 29, 1998
compared to $1.6 million for the thirteen weeks ended May 30, 1997. This
increase was primarily attributable to a net increase in the amount of accounts
receivable sold under the facility.

         PROVISION FOR INCOME TAXES. Provision for income taxes decreased to
$4.4 million for the thirteen weeks ended May 29, 1998 from $6.9 million for
the thirteen weeks ended May 30, 1997. The Company's effective tax rate was
36.1% for the thirteen weeks ended May 29, 1998 compared to 40.2% for the
thirteen weeks ended May 30, 1997.



                                       9
<PAGE>   12



RESULTS OF OPERATIONS (CONT.)

Thirty-Nine Weeks Ended May 29, 1998 Compared to Thirty-Nine Weeks Ended 
May 30, 1997

         NET SALES. Net sales increased 1.5% to $790.4 million for the
thirty-nine weeks ended May 29, 1998 from $778.9 million for the thirty-nine
weeks ended May 30, 1997, primarily as a result of improved yarn sales.

         Apparel fabric sales decreased 2.1% to $524.0 million for the
thirty-nine weeks ended May 29, 1998 from $535.2 million for the thirty-nine
weeks ended May 30, 1997. This decrease in sales reflected a 2.9% increase in
yards sold, offset by a 4.9% decline in average selling prices. The decline in
average selling prices resulted from softening market prices caused by excess
inventories of fabrics and garments within the industry, as well as increased
production capacity of domestic and international suppliers.

         Greige and specialty fabric sales increased 4.1% to $52.8 million for
the thirty-nine weeks ended May 29, 1998 from $50.7 million for the thirty-nine
weeks ended May 30, 1997. This increase in sales reflected continued strong
demand for greige fabrics by the home furnishings, luggage and shoe industries.

         Yarn sales increased 10.7% to $213.6 million for the thirty-nine weeks
ended May 29, 1998 from $192.9 million for the thirty-nine weeks ended May 30,
1997. This increase reflected a 12.1% increase in pounds sold and a 1.2%
decrease in average selling prices for those pounds. Market prices for sales
yarns remained very competitive, reflecting continued excess production
capacity within the industry during the thirty-nine weeks ended May 29, 1998.

         COST OF GOODS SOLD. Cost of goods sold decreased 0.2% to $661.7
million for the thirty-nine weeks ended May 29, 1998 from $662.8 million for
the thirty-nine weeks ended May 30, 1997. Cost of goods sold as a percentage of
net sales decreased to 83.7% for the thirty-nine weeks ended May 29, 1998 from
85.1% for the thirty-nine weeks ended May 30, 1997, primarily due to improved
capacity utilization and lower raw material costs.

         SELLING AND ADMINISTRATIVE EXPENSES. Selling and administrative
expenses increased 5.5% to $35.8 million for the thirty-nine weeks ended May
29, 1998 from $33.9 million for the thirty-nine weeks ended May 30, 1997,
reflecting increased accrual of certain associate benefit expenses and
compensation expense related to redemption of stock options by certain current
and former associates of the company. Selling and administrative expenses as a
percentage of net sales increased to 4.5% for the thirty-nine weeks ended May
29, 1998 from 4.4% for the thirty-nine weeks ended May 30, 1997.

         FACILITY RESTRUCTURING. Charges incurred to consolidate manufacturing
facilities and dispose of certain inefficient equipment in the Company's
Graniteville, South Carolina operations were $2.7 million for the thirty-nine
weeks ended May 29, 1998.

         INTEREST EXPENSE, NET. Interest expense, net decreased 13.0% to $17.5
million for the thirty-nine weeks ended May 29, 1998 from $20.1 million for the
thirty-nine weeks ended May 30, 1997. This decrease reflected lower interest
rates and a lower average balance of outstanding borrowings during the
thirty-nine weeks ended May 29, 1998.

         DISCOUNT AND EXPENSES ON SALE OF RECEIVABLES. Discount and expenses on
sale of receivables were $5.5 million for the thirty-nine weeks ended May 29,
1998 compared to $4.8 million for the thirty-nine weeks ended May 30, 1997.
This increase was primarily attributable to the payment of bank fees relating
to the receivables securitization facility as well as a net increase in the
amount of accounts receivable sold under the facility.



                                      10
<PAGE>   13

RESULTS OF OPERATIONS (CONT.)


         PROVISION FOR INCOME TAXES. Provision for income taxes increased to
$14.5 million for the thirty-nine weeks ended May 29, 1998 from $8.0 million
for the thirty-nine weeks ended May 30, 1997. The Company's effective tax rate
was 38.7% for the thirty-nine weeks ended May 29, 1998 compared to 40.2% for
the thirty-nine weeks ended May 30, 1997.


LIQUIDITY AND CAPITAL RESOURCES

         Net cash provided by operating activities was $31.6 million for the
thirty-nine weeks ended May 29, 1998. Principal working capital changes
included a $3.4 million decrease in Accounts Receivable, a $26.4 million
increase in Inventories, and a $1.6 million decrease in Accounts Payable and
Accrued Expenses. Investing activities were predominantly equipment purchases
and plant improvements of $47.2 million made in connection with the ongoing
modernization of the Company's manufacturing facilities. Financing activities
included a $20.5 million net advance under the Company's revolving line of
credit, purchase and retirement of treasury stock of $15.4 million, payment of
$4.0 million in dividends on outstanding common stock, and receipt of $9.0
million from the sale of additional accounts receivable under the
securitization facility.

         At May 29, 1998, the Company had borrowings of $135.0 million
outstanding under its revolving line of credit and $65.0 million of borrowing
availability thereunder.

         On May 10, 1998, the Company repurchased 592,000 shares of Class A
Common Stock for an aggregate purchase price of $15.4 million. These shares
were repurchased pursuant to a tender offer, distributed to all shareholders
and vested stock option holders of the Company's Class A Common Stock, to
purchase for cash up to $18.0 million worth of Class A Common Stock. All shares
repurchased have been canceled and reinstated as authorized but unissued shares
of Class A Common Stock.

         The Company's capital expenditures, aggregating $47.2 million for the
thirty-nine weeks ended May 29, 1998, were primarily related to the
construction of a new weaving facility in South Carolina and other equipment
purchases. Management estimates that capital expenditures for the balance of
fiscal 1998 will be approximately $18.0 million, and that such amounts will be
used primarily to upgrade weaving equipment and to improve fabric finishing
facilities.

         Management believes that cash generated from operations, together with
borrowings available under its revolving line of credit and proceeds received
in connection with sales of trade receivables, will be sufficient to meet the
Company's working capital and capital expenditure needs in the foreseeable
future. The Company will also continue to consider other options available to
it in connection with future working capital and capital expenditure needs,
including the issuance of additional debt and equity securities.



                                      11
<PAGE>   14

OTHER DATA


         The table below sets forth EBITDA of the Company for the periods
indicated. EBITDA is not presented as an alternative measure of operating
results or cash flow from operations (as determined in accordance with
generally accepted accounting principles), but because it is a widely accepted
financial indicator of the ability of a company to incur and service debt,
which is calculated by the Company as follows (amounts in thousands).



<TABLE>
<CAPTION>
                                                                 THIRTY-NINE WEEKS ENDED
                                                                -------------------------
                                                                  MAY 30,         MAY 29,   
                                                                   1997            1998
                                                                ----------      ---------
           <S>                                                  <C>             <C>
           Net income                                           $   11,937      $  22,919
           Interest expense                                         20,095         17,482
           Discount and expenses on sale of receivables              4,795          5,534
           Provision for income taxes                                8,040         14,480
           Depreciation and amortization                            30,730         29,805
           Loss attributable to investment in Oneita                 6,456             --
           Facility restructuring                                       --          2,699
           Net change in allowance to reduce carrying
                value of inventory to LIFO basis                    (3,600)        (1,050)
                                                                ----------      ---------

           EBITDA                                               $   78,453      $  91,869
                                                                ==========      =========
</TABLE>




ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK.

         Not Applicable.



                                      12
<PAGE>   15


                             AVONDALE INCORPORATED



  PART II - OTHER INFORMATION



Item 1      Legal Proceedings

            None


Item 2      Changes in Securities and Use of Proceeds
            
            None


Item 3      Defaults upon Senior Securities

            None


Item 4      Submission of Matters to a Vote of Security Holders
            
            None


Item 5      Other Information

            None


Item 6      Exhibits and Reports on Form 8-K
            
            (a)    Exhibits

                   27.1     Financial Data Schedule - Thirty-Nine weeks ended 
                            May 29.
                   
                   27.2     Financial Data Schedule - Thirty-Nine weeks ended 
                            May 30, 1997 (restated).

            (b)    Reports on Form 8-K

                   1.       On April 29, 1998, the Company filed a current 
                            report on Form 8-K regarding a change in the 
                            Company's certifying accountant.



                                      13
<PAGE>   16
                                   SIGNATURE



         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.




                        AVONDALE INCORPORATED




                       
                        By:      /S/ G. STEPHEN FELKER
                                 -----------------------------------------------
                                 G. Stephen Felker
                                 Chairman, President and Chief Executive Officer





                        By:      /S/ JACK R. ALTHERR, JR.
                                 -----------------------------------------------
                                 Jack R. Altherr, Jr.
                                 Vice Chairman and Chief Financial Officer








Date:      July 9, 1998
           ------------


                                      14