<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 quarterly period ended July 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 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 August 26, 1998, 493,232,408 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 Income --                     3
                   13 and 26 weeks ended July 29, 1998 and
                   July 30, 1997

                   Consolidated Balance Sheets--                            4
                   July 29, 1998, July 30, 1997 and
                   January 28, 1998

                   Consolidated Statements of Cash Flows --                 5
                   26 weeks ended July 29, 1998 and
                   July 30, 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 4.            Submission of Matters to a Vote of Security Holders   11 - 12

Item 5.            Other Information                                        12

Item 6.            Exhibits and Reports on Form 8-K                         12

                   Signatures


                                       2
<PAGE>   3


PART I. FINANCIAL INFORMATION
ITEM 1. FINANCIAL STATEMENTS:

                                KMART CORPORATION
                        CONSOLIDATED STATEMENTS OF INCOME
                  (DOLLARS IN MILLIONS, EXCEPT PER SHARE DATA)
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                                                         13 WEEKS ENDED                    26 WEEKS ENDED
                                                              -----------------------------     ------------------------------
                                                               JULY 29,            JULY 30,         JULY 29,          JULY 30,
                                                                 1998                1997             1998              1997
                                                              ---------         -----------     ------------      ------------
<S>                                                           <C>               <C>             <C>               <C>   
Sales                                                         $   8,116         $     7,846     $     15,631      $     15,109
Cost of sales, buying and occupancy                               6,336               6,197           12,244            11,834
                                                              ---------         -----------     ------------      ------------
Gross margin                                                      1,780               1,649            3,387             3,275
Selling, general and administrative expenses                      1,561               1,497            3,010             2,988
Voluntary early retirement program                                   19                -                  19              -
                                                              ---------         -----------     ------------      ------------
Income before interest, income taxes and dividends on                                                                   
     convertible preferred securities of subsidiary                 200                 152              358               287
Interest expense, net                                                70                  92              144               190
Income tax provision                                                 38                  17               62                28
Dividends on convertible preferred securities of subsidiary,                                                            
    net of income taxes of $7, $7, $14, and $13                      12                  12               25                24
                                                              ---------         -----------     ------------      ------------
Net income                                                    $      80         $        31     $        127      $         45
                                                              =========         ===========     ============      ============


Basic income per common share                                 $    0.16         $      0.06     $       0.26      $       0.09
                                                              =========         ===========     ============      ============

Basic weighted average shares (millions)                          492.9               487.1            491.3             486.2



</TABLE>







          See accompanying Notes to Consolidated Financial Statements.



                                       3
<PAGE>   4



                                KMART CORPORATION
                           CONSOLIDATED BALANCE SHEETS
                              (DOLLARS IN MILLIONS)
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                                                            JULY 29,     JULY 30,   JANUARY 28,
                                                                              1998        1997         1998
                                                                            -------      -------      -------
<S>                                                                         <C>          <C>          <C>    
Current Assets:
    Cash and equivalents                                                    $   556      $   253      $   498
    Merchandise inventories                                                   6,808        6,819        6,367
    Other current assets                                                        673          889          611
                                                                            -------      -------      -------
Total current assets                                                          8,037        7,961        7,476

Property and equipment, net                                                   5,642        5,538        5,472
Property held for sale or financing                                             119          200          271
Other assets and deferred charges                                               328          595          339
                                                                            -------      -------      -------
Total Assets                                                                $14,126      $14,294      $13,558
                                                                            =======      =======      =======

Current Liabilities:
   Long-term debt due within one year                                       $    51      $   109      $    78
   Trade accounts payable                                                     2,334        2,033        1,923
   Accrued payroll and other liabilities                                      1,199        1,196        1,064
   Taxes other than income taxes                                                241          244          209
                                                                            -------      -------      -------
Total current liabilities                                                     3,825        3,582        3,274

Long-term debt and notes payable                                              1,636        2,191        1,725
Capital lease obligations                                                     1,136        1,389        1,179
Other long-term liabilities                                                     927          922          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 July 29, 1998)                                                    983          980          981
Common stock, 1,500,000,000 shares authorized; shares issued
    493,284,068, 487,545,870, and 488,811,271, respectively                     493          489          489
Capital in excess of par value                                                1,659        1,594        1,605
Retained earnings                                                             3,467        3,147        3,340
                                                                            -------      -------      -------
Total Liabilitites and Shareholders' Equity                                 $14,126      $14,294      $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>
                                                                            26 WEEKS ENDED
                                                                        ----------------------
                                                                        JULY 29,      JULY 30,
                                                                         1998          1997
                                                                        -------       -------
<S>                                                                     <C>           <C>  
CASH FLOWS FROM OPERATING ACTIVITIES:
     Net income                                                         $ 127         $  45
     Adjustments to reconcile net income to net cash
          provided by operating activities:
          Voluntary early retirement program                               19            -
          Depreciation and amortization                                   332           337
          Increase in accounts receivable                                 (65)          (12)
          Increase in operating supplies and prepaids                     (41)          (53)
          Increase in inventories                                        (441)         (465)
          Increase in accounts payable                                    411            24
          Deferred income taxes and taxes payable                         160            16
          Changes in certain assets, liabilities and other items          (40)          127
                                                                        -----         -----
     Net cash provided by operating activities                            462            19
                                                                        -----         -----

CASH FLOWS FROM INVESTING ACTIVITIES:
     Proceeds from divestitures                                            87           129
     Proceeds from real estate financing and other                         22            43
     Capital contributions from minority interests                         -            (55)
     Other - net                                                           (6)          (88)
     Capital expenditures                                                (406)         (178)
                                                                        -----         -----
     Net cash used for investing activities                              (303)         (149)
                                                                        -----         -----

CASH FLOWS FROM FINANCING ACTIVITIES:
     Changes in common stock                                               58            25
     Proceeds from issuance of long-term debt and notes payable             -           739
     Reduction in capital lease obligations                               (43)          (57)
     Reduction in long-term debt and notes payable                       (116)         (730)
                                                                        -----         -----
     Net cash used for financing activities                              (101)          (23)
                                                                        -----         -----

Net increase (decrease) in cash and equivalents                            58          (153)
Cash and equivalents at beginning of period                               498           406
                                                                        -----         -----
Cash and equivalents at end of period                                   $ 556         $ 253
                                                                        =====         =====
</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 July 30, 1997
consolidated balance sheet and cash flows have been made to conform to current
year presentation.


2.)      DIVESTITURE

         In February 1998, the Company's minority interest in Kmart Canada Co.
was purchased by Hudson's Bay Co. Under the terms of the purchase, Kmart
received approximately $8 million for its remaining equity interest in Kmart
Canada Co., along with $79 million for repayment of its 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 July 29, 1998, July 30, 1997
and January 28, 1998 were $467 million, $451 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 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 46 stores previously operated by Venture Stores, Inc. These
stores are being converted to the Big Kmart format and are scheduled to be
operational in the fourth quarter of 1998.







                                       6
<PAGE>   7

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


<TABLE>
<CAPTION>
                                                     13 WEEKS                     % CHANGE
                                            -------------------------     ----------------------------
                                            JULY 29,         JULY 30,                      COMPARABLE
     ($ Millions)                             1998            1997          ALL STORES       STORES
                                            --------         --------     ------------     -----------
<S>                                         <C>              <C>                 <C>           <C>
SALES               
     General Merchandise
         United States                      $ 8,116          $7,749              4.7           4.4
         International                          -                97           (100.0)          -
                                            -------          ------           
     Consolidated Sales                     $ 8,116          $7,846              3.4           4.4
                                            =======          ======
OPERATING INCOME
     United States                          $   200          $  151              
     International                              -                 1              
                                            -------          ------
     Consolidated Operating Income          $   200          $  152              
                                            =======          ======
</TABLE>

        SALES and comparable store sales increased 3.4% and 4.4%, respectively
for the 13 weeks ended July 29, 1998. The increases were primarily due to:
improved merchandise assortments; continued roll out of the Big Kmart format,
with 134 store conversions during the quarter; and execution of the Company's
competitive pricing strategy. Divisions showing particular strength for the
quarter included apparel, pharmacy, consumables, home electronics and
appliances, health and beauty, and home fashions. The Company closed 8 stores
and opened 2 stores during the second quarter.
        

        GROSS MARGIN, as a percentage of sales, was 21.9% and 21.0% for the 13
weeks ended July 29, 1998 and July 30, 1997, respectively. The increase in the
percentage reflects lower levels of apparel markdowns, partially offset by the
execution of the Company's competitive pricing strategy and growth in consumable
sales.
        
        SELLING, GENERAL AND ADMINISTRATIVE ("SG&A") EXPENSES, as a percentage
of sales, were 19.2% and 19.1%, for the 13 weeks ended July 29, 1998, and July
30, 1997, respectively. The 10 basis point increase, or $64 million, resulted 
primarily from increased Year 2000 compliance expenses, net advertising 
expenses and costs associated with closed stores.
        

        OPERATING INCOME for the 13 weeks ended July 29, 1998 was $200 million,
or 2.5% of sales, as compared to operating income of $152 million, or 1.9% of
sales, for the same period of the prior year. This increase was the result of
increased sales volumes and the increased profitability of the apparel division.
        

        NET INTEREST EXPENSE for the 13 weeks ended July 29, 1998 was $70 
million as compared to $92 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


<TABLE>
<CAPTION>
                                                      26 WEEKS                          % CHANGE
                                           ---------------------------          ---------------------------
                                            JULY 29,          JULY 30,                          COMPARABLE
     ($ Millions)                             1998              1997            ALL STORES        STORES
                                            --------          --------          ---------------------------      
<S>                                         <C>               <C>                    <C>           <C>
SALES
     General Merchandise
         United States                      $ 15,631          $ 14,810               5.5           5.2
         International                           -                 299            (100.0)          -
                                            --------          --------

     Consolidated Sales                     $ 15,631          $ 15,109               3.5           5.2
                                            ========          ========


OPERATING INCOME
     United States                          $    358          $    290              
     International                               -                  (3)             
                                            --------          --------

     Consolidated Operating Income          $    358          $    287              
                                            ========          ========
</TABLE>

        SALES and comparable store sales increased 3.5% and 5.2%, respectively
for the 26 weeks ended July 29, 1998. The increases were primarily due to:
improved merchandise assortments; continued roll out of the Big Kmart format,
with 252 store conversions during the period; and execution of the Company's
competitive pricing strategy. Divisions showing particular strength included
apparel, consumables, pharmacy, home electronics and appliances, health and
beauty, and home fashions. The Company operated a total of 2,114 stores as of
July 29, 1998 compared to 2,122 stores for the same period of the prior year.
The Company closed 24 stores and opened 2 stores during the period.

        GROSS MARGIN, as a percentage of sales, was 21.7% for both the 26 weeks
ended July 29, 1998 and July 30, 1997. This is attributable to increased margin
due to lower levels of apparel markdowns offset by the execution of the
Company's competitive pricing strategy and growth in consumable sales.
        

        SELLING, GENERAL AND ADMINISTRATIVE ("SG&A") EXPENSES, as a percentage
of sales, were 19.3% and 19.8%, for the 26 weeks ended July 29, 1998, and July
30, 1997, respectively. The 50 basis point decrease, or $22 million, resulted 
primarily from the sale of international operations and increased leverage 
given additional sales volume offset by increased Year 2000 compliance
expenses and costs associated with closed stores.
        
        OPERATING INCOME for the 26 weeks ended July 29, 1998 was $358 million,
or 2.3% of sales, as compared to operating income of $287 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,
continued leveraging of SG&A expenses and the sale of the remaining interest in
Kmart Canada Co.
        
        NET INTEREST EXPENSE for the 26 weeks ended July 29, 1998 was $144
million as compared to $190 million for the same period of the prior year. Net
interest expense decreased as a result of lower levels of borrowings, primarily
attributable to the payoff of the Term Loan 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 $4,212, $4,379 and $4,202 million at July 29, 1998, July 30, 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 second
quarter of 1998.

         Net cash provided by operating activities for the 26 weeks ended July
29, 1998 was $462 million as compared to $19 million for the same period in
1997. The increase in cash was primarily the result of increased earnings,
improved inventory leverage and receipt of federal tax refunds.

         Net cash used for investing activities was $303 million for the 26
weeks ended July 29, 1998 compared to $149 million for the same period in 1997.
The increase in cash used by investing activities was primarily the result of
increased capital expenditures.

         Net cash used for financing activities was $101 million for the 26
weeks ended July 29, 1998 compared to $23 million for the same period in 1997.
Cash used for financing during 1997 was the result of paying down the Company's
remaining balance on the Term Loan as well as payments on certain mortgages and
medium term notes. These amounts were partially offset by the issuance of $335
million in Commercial Mortgage Pass Through Securities.

         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 Company's Year 2000 compliance program consists of four phases, 
(1) inventory and assessment, (2) remediation and unit testing, (3) return to
production and (4) integration testing.  The Company has completed the inventory
and assessment phase for essentially all of its computer systems and
applications with the goal of having substantially all business critical
applications returned to production during the fourth quarter of 1998.
Integration tests are planned for the second and third quarters of 1999. 
        
         The Company has initiated formal communication with significant
suppliers to evaluate their Year 2000 compliance.  Most of these parties have
stated their ability to supply the Company will not be affected by the Year
2000 issue.  However, the Company cannot assure timely compliance of third
parties and may be adversely affected by failure of a significant third party
to become Year 2000 compliant.

         The total costs of modifying the Company's current systems are not
expected to have a material adverse impact on the Company's financial position,
results of operations or cash flows in future periods.  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 occurence to be
reasonably likely.  Should the outlook for completion of the compliance program
change, management will develop appropriate contingency plans to address any
non-compliance issues.



                                       9
<PAGE>   10
                                KMART CORPORATION
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
                        FINANCIAL CONDITION -- CONTINUED


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 the first half of the year, the Company
purchased approximately 437,700 shares at an average price of $18.44 per share.

         Effective April 3, 1998, the American Institute of Certified Public
Accountants' Accounting Standards Executive Committee issued Statement of
Position ("SOP") No. 98-5, "Reporting on the Costs of Start-Up Activities",
which requires that pre-opening costs and related organization costs be expensed
as incurred. This statement does not have a material effect on the Company's
financial position or results of operations.

CAUTIONARY STATEMENT REGARDING FORWARD-LOOKING INFORMATION

         Statements, other than those based on historical facts, including the
discussion of management expectations for Year 2000 compliance, which address
activities, events, or developments that the Company expects or anticipates may
occur in the future are forward-looking statements which are based upon a number
of assumptions concerning future conditions that may ultimately prove to be
inaccurate. Actual events and results may materially differ from anticipated
results described in such statements. The Company's ability to achieve such
results is subject to certain risks and uncertainties, including, but not
limited to, economic and weather conditions which affect buying patterns of the
Company's customers, changes in consumer spending and the Company's ability to
anticipate buying patterns and implement appropriate inventory strategies,
continued availability of capital and financing, competitive factors 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 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

The following information is furnished with respect to the Annual Meeting of
Shareholders of Kmart Corporation held during May 1998:

(a)      Annual Meeting was held on May 19, 1998.

(b)      Not Applicable

(c)      Proposal 1 

         At such meeting all of the nominees for election as directors were
         elected for the term of office set forth below:

         The votes cast with respect to each nominee for election as a director
         were as follows:

<TABLE>
<CAPTION>
                                                                                                   Votes to Withhold
                                         Year When Term of                 Votes for             Authority to Vote for
                  Nominee                  Office Expires                 the Nominee                   Nominee
                  -------                  --------------                 -----------                   -------
<S>                                      <C>                              <C>                          <C>
           Lilyan H. Affinito                   2001                      427,979,688                  9,119,853
           Richard G. Cline                     2001                      428,153,810                  8,945,731
           Willie D. Davis                      2001                      428,042,475                  9,057,066
           Joseph P. Flannery                   2001                      427,915,731                  9,183,810
</TABLE>

         A plurality of the votes cast were in favor of all nominees, and they
         were therefore elected.

         Proposal 2

         The votes cast to ratify the appointment of Price Waterhouse LLP* as
         independent accountants of the Company for the 1998 fiscal year, were
         as follows:

                                       For --       433,564,235
                                   Against --         1,941,183
                                   Abstain --         1,594,122

         A majority of the votes cast were in favor of proposal 2 and,
         therefore, it was passed.

         Proposal 3

         The votes cast for a stockholder proposal to prepare a report on vendor
         monitoring describing the Company's actions to ensure that it does not
         and will not do business with foreign suppliers who manufacture items
         for sale in the United States using forced labor, convict labor or
         illegal child labor, or who fail to satisfy all applicable laws and
         standards protecting their employees' wages, benefits, working
         conditions, freedom of associations and other rights, were as follows:

                                       For --        29,360,824
                                   Against --       303,503,574
                                   Abstain --        28,176,818
                                   No Vote --        76,058,324

         A majority of the votes cast were not in favor of proposal 3 and,
         therefore, it was not passed.

         * Effective July 1, 1998, Price Waterhouse LLP merged with Coopers and
         Lybrand LLP to form PricewaterhouseCoopers LLP.


                                       11
<PAGE>   12

         Proposal 4

         The votes cast for a stockholder proposal to amend the Articles of
         Incorporation of Kmart, Inc. to eliminate the classification of the
         directors of the Company, were as follows:

                                       For --       150,937,458
                                   Against --       205,379,506
                                   Abstain --         4,728,874
                                   No Vote --        76,053,703

         A majority of the votes cast were not in favor of proposal 4 and,
         therefore, it was not passed.


ITEM 5.  OTHER INFORMATION

         Pursuant to Article I, Section 8 of the Company's Bylaws, proposals of
         stockholders intended to be presented at the 1999 Annual Meeting of
         Stockholders (other than stockholder proposals set forth in the
         Company's proxy statement) must be received by the Secretary of the
         Company on or before February 17, 1999 unless the Meeting is not held
         within eight days of May 18, 1999. In the latter case, if less than 100
         days notice or public disclosure of the Annual Meeting date is given,
         notice of the proposal must be received by the Secretary not later than
         the tenth day following the date notice or public disclosure of the
         Meeting date is given to stockholders.


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

(b)      Reports on Form 8-K: No reports were filed on Form 8-K by the
         Registrant during the 13 weeks ended July 29, 1998.





                                       12
<PAGE>   13



                                   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:           September 14, 1998
 
                                                Kmart Corporation
                                            ------------------------------------
                                                    (Registrant)


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








                                       13
<PAGE>   14



                                 Exhibit Index
                                 -------------


Exhibit No.                    Description
-----------                    -----------

    11                         Information on Computation of Per
                               Share Earnings

    27                         Financial Data Schedule