<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
   
                                 FORM 10-Q/A
    


X   QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(d) OF THE SECURITIES
-   EXCHANGE ACT OF 1934
For the quarterly period ended October 28, 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 No. 1-327
                    -----
                                KMART CORPORATION
                                -----------------
             (Exact name of registrant as specified in its charter)


             Michigan                                         38-0729500
--------------------------------------------------------------------------------
 (State or other jurisdiction of                           (I.R.S. Employer
  incorporation or organization)                          Identification No.)

3100 West Big Beaver Road - Troy, Michigan                      48084
--------------------------------------------------------------------------------
         (Address of principal executive offices)             (Zip Code)

  Registrant's telephone number, including area code       (248) 643-1000
                                                           --------------


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
                                  --------       -------


As of November 25, 1998, 492,931,875 shares of Common Stock of the Registrant
were outstanding.







                                       1
<PAGE>   2


INDEX

PART I            FINANCIAL INFORMATION                                  PAGE
------            ---------------------                                  ----

Item 1.           Financial Statements


                  Consolidated Statements of Earnings --                   3
                  13 and 39 weeks ended October 28, 1998 and
                  October 29, 1997

                  Consolidated Balance Sheets --                           4
                  October 28, 1998, October 29, 1997 and
                  January 28, 1998

                  Consolidated Statements of Cash Flows--                  5
                  39 weeks ended October 28, 1998 and
                  October 29, 1997

                  Notes to Consolidated Financial                          6
                  Statements

Item 2.           Management's Discussion and Analysis of Results of    7-10
                  Operations and Financial
                  Condition

PART II           OTHER INFORMATION
-------           -----------------


Item 6.           Exhibits and Reports on Form 8-K                        11

                  Signatures

















                                       2


<PAGE>   3


PART I. FINANCIAL INFORMATION
Item 1. Financial Statements:

                                KMART CORPORATION
                       CONSOLIDATED STATEMENTS OF EARNINGS
                  (Dollars in millions, except per share data)
                                   (Unaudited)
<TABLE>
<CAPTION>

                                                                       13 WEEKS ENDED                           39 WEEKS ENDED
                                                              -------------------------------         ------------------------------
                                                               OCTOBER 28,        OCTOBER 29,          OCTOBER 28,       OCTOBER 29,
                                                                  1998                1997                1998             1997
                                                              ------------       ------------         ------------      ------------
<S>                                                               <C>               <C>                  <C>               <C>
Sales                                                             $ 7,642           $ 7,315              $23,273           $22,424
Cost of sales, buying and occupancy                                 5,954             5,683               18,198            17,517
                                                                  -------           -------              -------           -------
Gross margin                                                        1,688             1,632                5,075             4,907
Selling, general and administrative expenses                        1,540             1,492                4,550             4,480
Voluntary early retirement program                                   --                --                     19              --
                                                                  -------           -------              -------           -------
Income before interest, income taxes and dividends on                                                             
     convertible preferred securities of subsidiary                   148               140                  506               427
Interest expense, net                                                  76                96                  220               286
Income tax provision                                                   21                13                   83                41
Dividends on convertible preferred securities of subsidiary,                                                      
    net of income taxes of $6, $7, $20, and $20, respectively          13                13                   38                37
                                                                  -------           -------              -------           -------
Net income                                                        $    38           $    18              $   165           $    63
                                                                  =======           =======              =======           =======


Basic income per common share                                     $  0.08           $  0.04              $  0.34           $  0.13
                                                                  =======           =======              =======           =======

Basic weighted average shares (millions)                            492.8             488.0                491.7             486.8
</TABLE>





          See accompanying Notes to Consolidated Financial Statements.













                                       3

<PAGE>   4


                                KMART CORPORATION
                           CONSOLIDATED BALANCE SHEETS
                              (Dollars in millions)
                                   (Unaudited)
<TABLE>
<CAPTION>
                                                                         OCTOBER 28,        OCTOBER 29,       JANUARY 28,
                                                                            1998               1997              1998
                                                                         -----------        ------------      -----------
<S>                                                                       <C>                <C>               <C>
Current Assets:
    Cash and equivalents                                                  $   350            $   280           $   498
    Merchandise inventories                                                 8,060              7,793             6,367
    Other current assets                                                      844              1,015               611
                                                                          --------           --------          --------
Total current assets                                                        9,254              9,088             7,476

Property and equipment, net                                                 5,852              5,442             5,472
Other assets and deferred charges                                             443                505               610
                                                                          --------           --------          --------
Total Assets                                                              $15,549            $15,035           $13,558
                                                                          ========           ========          ========

Current Liabilities:                                                                                          
   Long-term debt due within one year                                     $    60            $    76           $    78
   Trade accounts payable                                                   3,019              2,824             1,923
   Accrued payroll                                                            855                838               863
   Taxes other than income taxes                                              240                250               209
   Other current liabilities                                                  387                179               201
                                                                          --------           --------          --------
Total current liabilities                                                   4,561              4,167             3,274

Long-term debt and notes payable                                            2,313              2,347             1,725
Capital lease obligations                                                   1,114              1,362             1,179
Other long-term liabilities                                                   928                921               965
Company obligated mandatorily redeemable convertible preferred                                                
    securities of a subsidiary trust holding solely 7 3/4% convertible                                           
    junior subordinated debentures of Kmart (redemption value                                                 
    $1,000 at October 28, 1998)                                               983                979               981
Common stock, 1,500,000,000 shares authorized; shares issued                                                  
    492,752,144, 488,367,468, and 488,811,271, respectively                   493                489               489
Capital in excess of par value                                              1,654              1,605             1,605
Retained earnings                                                           3,503              3,165             3,340
                                                                          --------           --------          --------
Total Liabilities and Shareholders' Equity                                $15,549            $15,035           $13,558
                                                                          ========           ========          ========
</TABLE>








          See accompanying Notes to Consolidated Financial Statements.







                                       4

<PAGE>   5


                                KMART CORPORATION
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                              (Dollars in millions)
                                   (Unaudited)
<TABLE>
<CAPTION>
                                                                                                  39 WEEKS ENDED
                                                                                           ------------------------------
                                                                                           OCTOBER 28,        OCTOBER 29,
                                                                                             1998               1997
                                                                                           -------------      -----------
<S>                                                                                        <C>                <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
      Net income                                                                           $  165             $   63
      Adjustments to reconcile net income to net cash                                                      
           used for operating activities:                                                                  
           Voluntary early retirement program                                                  19                  -
           Depreciation and amortization                                                      498                496
           Increase in accounts receivable                                                   (213)              (114)
           Increase in operating supplies and prepaids                                        (62)               (37)
           Increase in inventories                                                         (1,693)            (1,439)
           Increase in accounts payable                                                     1,096                815
           Deferred income taxes and taxes payable                                            156                 25
           Decrease in other long-term liabilities                                            (56)               (46)
           Changes in certain assets, liabilities and other items                              20                 85
                                                                                           ------             ------
      Net cash used for operating activities                                                  (70)              (152)
                                                                                           ------             ------

 CASH FLOWS FROM INVESTING ACTIVITIES:                                                                     
      Proceeds from divestitures                                                               87                145
      Proceeds from real estate transactions and other                                         23                413
      Capital contributions from minority interests                                             -                (55)
      Capital expenditures                                                                   (745)              (489)
      Other                                                                                     -                (70)
                                                                                           ------             ------
      Net cash used for investing activities                                                 (635)               (56)
                                                                                           ------             ------

 CASH FLOWS FROM FINANCING ACTIVITIES:                                                                     
      Proceeds from issuance of long-term debt and notes payable                              750                901
      Changes in common stock                                                                  52                 36
      Payments on capital lease obligations                                                   (65)               (85)
      Payments on long-term debt and notes payable                                           (180)              (770)
                                                                                           ------             ------
      Net cash provided by financing activities                                               557                 82
                                                                                           ------             ------

 Net change in cash and equivalents                                                          (148)              (126)
 Cash and equivalents at beginning of period                                                  498                406
                                                                                           ------             ------
 Cash and equivalents at end of period                                                     $  350             $  280
                                                                                           ======             ======
</TABLE>






          See accompanying Notes to Consolidated Financial Statements.









                                       5

<PAGE>   6


                                KMART CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)

1.)  BASIS OF PRESENTATION

         These interim unaudited consolidated financial statements have been
prepared in accordance with the rules and regulations of the Securities and
Exchange Commission, and, in the opinion of management, reflect all adjustments
(which include normal recurring adjustments) necessary for a fair statement of
the results for the interim periods. These consolidated financial statements
should be read in conjunction with the financial statements and the notes
thereto included in the Company's 1997 Annual Report and Form 10-K filed for the
fiscal year ended January 28, 1998.

         Certain reclassifications of the January 28, 1998 and October 29, 1997
financial statements have been made to conform to current year presentation.


2.)      DIVESTITURE

         In February 1998, Hudson's Bay Co. purchased the Company's minority
interest in Kmart Canada Co. Under the terms of the purchase, Kmart received
approximately $8 million for the remaining equity interest in Kmart Canada Co.,
along with $79 million for repayment of an outstanding note and debentures.


3.)      INVENTORIES AND COST OF MERCHANDISE SOLD

         A substantial portion of the Company's inventory is accounted for using
the last-in, first-out (LIFO) method. Since LIFO costs can only be determined at
the end of each fiscal year when inflation rates and inventory levels are
finalized, estimates are used for LIFO purposes in the interim consolidated
financial statements. Inventories valued on LIFO at October 28, 1998, October
29, 1997 and January 28, 1998 were $465 million, $447 million and $457 million
lower than the amounts that would have been reported under the first-in,
first-out (FIFO) method, respectively.

4.)      PENSION PLANS

         In the second quarter of 1998, the Company announced and completed a
Voluntary Early Retirement Program for certain Kmart distribution center
associates. The Company recorded a charge of $19 million ($13 million after tax)
based on the acceptance of the program by associates. Payouts under this program
will be fully funded through existing pension plan assets.

5.)      LEASE ACQUISITIONS

         On May 1, 1998, the Company entered into an agreement with Kimco Realty
Corporation to lease stores previously operated by Venture Stores, Inc.
Forty-five of these locations have been converted to the Big Kmart format and
operations commenced on October 29, 1998.












                                       6


<PAGE>   7


Item 2
                                KMART CORPORATION
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
                               FINANCIAL CONDITION


RESULTS OF OPERATIONS
<TABLE>
<CAPTION>
                                                       13 WEEKS                          % CHANGE
                                          ----------------------------    -------------------------------------
      ($ Millions)                        OCTOBER 28,    OCTOBER 29,                               COMPARABLE
                                               1998         1997              ALL STORES             STORES
                                          -----------   --------------    --------------          -------------
<S>                                         <C>            <C>                   <C>                   <C>
SALES                                       $7,642         $7,315                4.5                   4.2
                                            ======         ======

OPERATING INCOME                            $  148         $  140
                                            ======         ======
</TABLE>



         SALES and comparable store sales increased 4.5% and 4.2%, respectively
for the 13 weeks ended October 28, 1998. The increases were primarily due to:
improved merchandise assortments; continued roll out of the Big Kmart format,
with 267 store conversions during the quarter; and execution of the Company's
competitive pricing strategy. Divisions showing particular strength for the
quarter included consumables, home appliances and electronics, pharmacy, health
and beauty, and home decor. The Company closed 11 stores and opened 6 stores
during the third quarter.


         GROSS MARGIN, as a percentage of sales, was 22.1% and 22.3% for the 13
weeks ended October 28, 1998 and October 29, 1997, respectively. The decrease in
the percentage reflects the execution of the Company's competitive pricing
strategy and the continued expansion of the Big Kmart format which emphasizes
lower margined consumables, partially offset by improved margins resulting from
increased import and private label goods.


         SELLING, GENERAL AND ADMINISTRATIVE ("SG&A") EXPENSES, as a percentage
of sales, were 20.1% and 20.4%, for the 13 weeks ended October 28, 1998, and
October 29, 1997, respectively. The 30 basis point decrease resulted primarily
from increased expense leverage given additional sales volume.


         OPERATING INCOME for the 13 weeks ended October 28, 1998 was $148
million, or 2.0% of sales, as compared to operating income of $140 million, or
1.9% of sales, for the same period of the prior year. This increase was the
result of increased sales volumes, improved profitability of the apparel
division despite lower sales volumes and the leveraging of SG&A expenses.


         NET INTEREST EXPENSE for the 13 weeks ended October 28, 1998 was $76
million as compared to $96 million for the same period of the prior year. Net
interest expense decreased as a result of lower levels of borrowings and
increased investment income. See "Liquidity and Financial Condition".












                                       7

<PAGE>   8




                                KMART CORPORATION
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
                        FINANCIAL CONDITION -- Continued


RESULTS OF OPERATIONS
<TABLE>
<CAPTION>

                                                       39 WEEKS                          % CHANGE
                                          ----------------------------    -------------------------------------
      ($ millions)                        OCTOBER 28,    OCTOBER 29,                               COMPARABLE
                                               1998         1997              ALL STORES             STORES
                                          -----------   --------------    ---------------         -------------
<S>                                         <C>           <C>                  <C>                     <C>
SALES
      United States                         $23,273       $22,125                 5.2                  4.8
      International                               -           299              (100.0)                   -
                                            -------       -------
      Consolidated Sales                    $23,273       $22,424                 3.8                  4.8
                                            =======       =======

OPERATING INCOME
      United States                         $   506       $   430
      International                               -            (3)
                                            -------       -------
      Consolidated Operating Income         $   506       $   427
                                            =======       =======
</TABLE>


         SALES and comparable store sales increased 3.8% and 4.8%, respectively,
for the 39 weeks ended October 28, 1998. The increases were primarily due to:
improved merchandise assortments; continued roll out of the Big Kmart format,
with 519 store conversions during the period; and execution of the Company's
competitive pricing strategy. Divisions showing particular strength included
consumables, pharmacy, home appliances and electronics and apparel. The Company
operated a total of 2,109 stores as of October 28, 1998 compared to 2,121 stores
for the same period of the prior year. The Company closed 35 stores and opened 8
stores during the period.


         GROSS MARGIN, as a percentage of sales, was 21.8% and 21.9% for the 39
weeks ended October 28, 1998 and October 29, 1997, respectively. This decrease
is attributable to the execution of the Company's competitive pricing strategy
and growth in lower margined sales categories such as consumables, partially
offset by improved margins resulting from increased import and private label
goods.


         SELLING, GENERAL AND ADMINISTRATIVE ("SG&A") EXPENSES, as a percentage
of sales, were 19.5% and 20.0%, for the 39 weeks ended October 28, 1998, and
October 29, 1997, respectively. The 50 basis point decrease resulted primarily
from the sale of international operations and increased expense leverage given
additional sales volume, offset by increased Year 2000 compliance expenses.


         OPERATING INCOME for the 39 weeks ended October 28, 1998 was $506
million, or 2.2% of sales, as compared to operating income of $427 million, or
1.9% of sales, for the same period of the prior year. This increase was the
result of increased sales volumes, improved profitability of the apparel
division and continued leveraging of SG&A expenses.


         NET INTEREST EXPENSE for the 39 weeks ended October 28, 1998 was $220
million as compared to $286 million for the same period of the prior year. Net
interest expense decreased as a result of lower levels of borrowings and
increased investment income. See "Liquidity and Financial Condition".







                                       8



<PAGE>   9


                                KMART CORPORATION
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
                        FINANCIAL CONDITION -- Continued

LIQUIDITY AND FINANCIAL CONDITION

         Kmart's primary sources of working capital are cash flows from
operations and borrowings under its credit facilities. The Company had working
capital of $4,693, $4,921 and $4,202 million at October 28, 1998, October 29,
1997, and January 28, 1998, respectively. The Company's working capital
fluctuates in relation to profitability, seasonal inventory levels net of trade
accounts payable and the level of store openings and closings.

         In March 1998, the collateral securing the Company's borrowings under
the Revolving Credit Agreement was released. The Company continued to be in
compliance with all covenants contained in the Agreement during the third
quarter of 1998.

         Net cash used for operating activities for the 39 weeks ended October
28, 1998 was $70 million as compared to $152 million for the same period in
1997. The decrease in cash used was primarily the result of increased earnings,
a decrease in cash used for inventory net of accounts payable and receipt of
federal tax refunds.

         Net cash used for investing activities was $635 million for the 39
weeks ended October 28, 1998 compared to $56 million for the same period in
1997. The increase in cash used by investing activities was primarily the result
of increased capital expenditures and a reduced level of proceeds from real
estate transactions.

         Net cash provided by financing activities was $557 million for the 39
weeks ended October 28, 1998 compared to $82 million for the same period in
1997. The increase in cash was primarily a result of the lower levels of debt
repayment in 1998 due to repayment of the remaining balance on the Term Loan in
1997.

         Management believes the funds generated by operations, together with
funds available under existing credit arrangements, are sufficient to meet the
Company's currently anticipated funding requirements.

YEAR 2000

         The Year 2000 statement set forth below is a Year 2000 Readiness
Disclosure, pursuant to the Year 2000 Information and Readiness Disclosure Act,
Public Law No. 105-271. Please note that, for purposes of any action brought
under the securities laws, as that term is defined in section 3(a)(47) of the
Securities Exchange Act of 1934 (15 U.S.C. 78c(a)(47)), the Year 2000
Information and Readiness Disclosure Act does not apply to any statements
contained in any documents or materials filed with the Securities and Exchange
Commission, or with Federal banking regulators, pursuant to section 12(i) of the
Securities Exchange Act of 1934 (15 U.S.C. 78l(i)), or disclosures or writing
that when made accompanied the solicitation of an offer or sale of securities.

         The Company's Year 2000 Compliance Program consists of four phases, (I)
inventory and assessment, (II) remediation and unit testing, (III) return to
production and (IV) integration testing. For information technology systems, the
Company has substantially completed phase I and has completed approximately 85
percent of phases II and III. The Company anticipates having substantially all
remaining business critical applications returned to production during the
fourth quarter of 1998. Integration tests are planned for the second, third and,
if necessary, the fourth quarters of 1999.

         The Company has initiated a formal communication program with
significant vendors to evaluate their Year 2000 compliance, and is assessing
their responses to the Company's Year 2000 readiness questionnaire.
Approximately 85 percent of significant merchandise vendors have responded most
to the effect that their ability to supply the Company will not be affected by
the Year 2000 issue. Although the Company values its relationships with
significant vendors, should such a vendor become unable to deliver merchandise
or services, substitute merchandise for many of the goods the Company sells and
substitutes for many of the services it receives can be obtained from other
vendors. However, the Company cannot assure timely compliance of vendors and may
be adversely affected by failure of a significant vendor to supply merchandise
or services due to Year 2000 compliance failures.


                                       9

<PAGE>   10


                                KMART CORPORATION
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
                        FINANCIAL CONDITION -- Continued

YEAR 2000 (continued)

         Should the Company not successfully complete a significant portion of
its Year 2000 Compliance Program, its financial condition may be materially
adversely impacted; however, management does not consider the possibility of
such an occurrence to be likely. The Company anticipates that the most
reasonably likely worst case scenarios include, but are not limited to, loss of
communication with stores, loss of electric power and inability to process
transactions or engage in similar normal business activity. Certain contingency
plans have been or will be created, such as installation of backup power
supplies and around-the-clock support teams. Despite these contingency plans,
the Company may be adversely affected by failure of a significant third party
(such as suppliers of utilities, communication, transportation, banking and
other services) to become Year 2000 compliant. In addition, due to the
uncertainty of the effect of Year 2000 failures on our customers, we are unable
to assess the effect these failures will have on consumer spending or on returns
of merchandise that may contain hardware or software components. As a result,
the Company cannot estimate the impact of these events on the Company's results
of operations, liquidity or financial condition.

         The total cost of the Company's Year 2000 Compliance Program is
estimated at $75 million, with $5 million incurred in 1997, and $33 million
incurred year-to-date. Estimated costs for fiscal 1998 total $43 million and are
being funded through operating cash flows. Certain information technology
projects have been delayed as a result of the Company's Year 2000 compliance
effort. Estimated future expenditures and the delay of information technology
projects are not expected to have a material adverse effect on the Company's
financial position, results of operations or cash flows.

         Estimated costs of the Company's Year 2000 Compliance Program and
projected completion dates are based on management's best estimates of future
events and are forward-looking statements that may be updated as additional
information becomes available. Readers are cautioned that forward-looking
statements contained herein should be read in conjunction with the Company's
disclosures under the heading "Cautionary Statement Regarding Forward-looking
Information" following this disclosure.

OTHER MATTERS

   
         As of the end of 1997, the board of directors approved the repurchase
of up to 2,000,000 shares of the Company's common stock to be used to fund the
Company's employee benefit plans. During 1998, the Company purchased
approximately 1,937,700 shares at a cost of $30.4 million.
    

CAUTIONARY STATEMENT REGARDING FORWARD-LOOKING INFORMATION

         This quarterly report includes forward-looking statements within the
meaning of the Private Securities Litigation Reform Act of 1995. Forward-looking
statements, including the discussion of management expectations for Year 2000
compliance, involve certain risks and uncertainties that may cause actual future
results to differ materially from those contemplated, projected, estimated or
budgeted in such forward-looking statements. Factors that may impact
forward-looking statements include, but are not limited to, the following:
economic and weather conditions which affect buying patterns of the Company's
customers, changes in consumer spending, the Company's ability to anticipate
buying patterns and implement appropriate inventory strategies, continued
availability of capital and financing, and competitive and other factors
affecting business beyond the Company's control. Consequently, all of the
forward-looking statements are qualified by these cautionary statements and
there can be no assurance that the results or developments anticipated by the
Company will be realized or that they will have the expected effects on the
Company or its business or operations.






                                       10


<PAGE>   11


PART II. OTHER INFORMATION


Item 6.  EXHIBITS AND REPORTS ON FORM 8-K

(a)      The following exhibits are filed as a part of this report:

         Exhibit 11 - Information on Computation of Per Share Earnings
         Exhibit 27 - Financial Data Schedule
         Exhibit 99 - Amendment to Employment Agreement

(b)      Reports on Form 8-K: No reports were filed on Form 8-K by the
         Registrant during the 13 weeks ended October 28, 1998.






















                                       11

<PAGE>   12


                                   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.

The signatory hereby acknowledges and adopts the typed form of his name in the
electronic filing of this document with the Securities and Exchange Commission.



















                     Date:                  December 7, 1998
                                            Kmart Corporation
                               ------------------------------------------------
                                               (Registrant)


                     By:                   /S/ M.E. Welch, III
                               ------------------------------------------------
                                               M.E. Welch, III
                                          SENIOR VICE PRESIDENT AND
                                           CHIEF FINANCIAL OFFICER
                                          (Duly Authorized Officer,
                                        Principal Financial Officer)

                     By:                  /S/ Lois M. Connelly
                               ------------------------------------------------
                                              Lois M. Connelly
                                         VICE PRESIDENT, CONTROLLER
                                          (Duly Authorized Officer,
                                        Principal Accounting Officer)



   



                                       12