<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 April 28, 1999

                                       OR

     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
---  EXCHANGE ACT OF 1934
For the transition period from           to
                              ----------    ----------

Commission File 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 April 28,1999, 495,076,689 shares of Common Stock of the Registrant were
outstanding.





<PAGE>   2

                                      INDEX

PART I         FINANCIAL INFORMATION                                    PAGE

Item 1.        Financial Statements


               Consolidated Statements of Earnings --                     3
               13 weeks ended April 28, 1999 and
               April 29, 1998

               Consolidated Balance Sheets--                              4
               April 28, 1999, April 29, 1998 and
               January 27, 1999

               Consolidated Statements of Cash Flows --                   5
               13 weeks ended April 28, 1999 and
               April 29, 1998

               Notes to Consolidated Financial                          6 - 8
               Statements

Item 2.        Management's Discussion and Analysis of Results of       9 - 12
               Operations and Financial
               Condition

PART II        OTHER INFORMATION


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

               Signatures                                                14






                                       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
                                                                     ----------------------------------
                                                                       APRIL 28,            APRIL 29,
                                                                         1999                 1998
                                                                     -------------       --------------
<S>                                                                  <C>                 <C>
  Sales                                                              $       8,144       $        7,515
  Cost of sales, buying and occupancy                                        6,417                5,908
                                                                     -------------       --------------
  Gross margin                                                               1,727                1,607

  Selling, general and administrative expenses                               1,541                1,449
                                                                     -------------       --------------

  Income before interest, income taxes and dividends on
     convertible preferred securities of subsidiary                            186                  158

  Interest expense, net                                                         66                   74

  Income tax provision                                                          40                   24

  Dividends on convertible preferred securities of subsidiary,
    net of income taxes of $7 and $7                                            13                   13
                                                                     -------------       --------------

  Net income                                                         $          67       $           47
                                                                     =============       ==============


  Basic income per common share                                      $        0.14       $         0.10
                                                                     =============       ==============
  Diluted income per common share                                    $        0.14       $         0.10
                                                                     =============       ==============

  Basic weighted average shares (millions)                                   494.1                489.7

  Diluted weighted average shares (millions)                                 567.1                562.3

</TABLE>










          See accompanying Notes to Consolidated Financial Statements.

                                       3
<PAGE>   4


                                KMART CORPORATION
                           CONSOLIDATED BALANCE SHEETS
                             (DOLLARS IN MILLIONS)
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                                                                       APRIL 28,         APRIL 29,      JANUARY 27,
                                                                                         1999              1998            1999
                                                                                       ---------        ---------       -----------
<S>                                                                                     <C>              <C>              <C>
Current Assets:
    Cash and cash equivalents                                                           $   619          $   733          $   710

    Merchandise inventories                                                               7,445            6,884            6,536

    Other current assets                                                                    657              643              584
                                                                                        -------          -------          -------

Total current assets                                                                      8,721            8,260            7,830


Property and equipment, net                                                               5,965            5,558            5,914

Other assets and deferred charges                                                           441              433              422
                                                                                        -------          -------          -------

Total Assets                                                                            $15,127          $14,251          $14,166
                                                                                        =======          =======          =======

Current Liabilities:
   Long-term debt due within one year                                                   $    77          $    77          $    77
   Trade accounts payable                                                                 3,040            2,589            2,047

   Accrued payroll and other liabilities                                                  1,243            1,034            1,359

   Taxes other than income taxes                                                            245              227              208
                                                                                        -------          -------          -------

Total current liabilities                                                                 4,605            3,927            3,691


Long-term debt and notes payable                                                          1,529            1,696            1,538

Capital lease obligations                                                                 1,073            1,158            1,091

Other long-term liabilities                                                                 866              968              883

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 April 28, 1999)                         985              982              984


Common stock, $1 par value, 1,500,000,000 shares authorized;
    495,076,689, 492,104,491, and 493,358,504, shares issued                                495              492              493

Capital in excess of par value                                                            1,688            1,641            1,667

Retained earnings                                                                         3,886            3,387            3,819
                                                                                        -------          -------          -------

Total Liabilities and Shareholders' Equity                                              $15,127          $14,251          $14,166
                                                                                        =======          =======          =======
</TABLE>





          See accompanying Notes to Consolidated Financial Statements.

                                       4
<PAGE>   5


                                KMART CORPORATION
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                              (DOLLARS IN MILLIONS)
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                                                          13 WEEKS ENDED
                                                                      -------------------------
                                                                      APRIL 28,       APRIL 29,
                                                                         1999            1998
                                                                      ---------       ---------
<S>                                                                     <C>             <C>
CASH FLOW FROM OPERATING ACTIVITIES
     Net income                                                         $  67           $  47
     Adjustments to reconcile net income to net cash
          provided by operating activities:
          Depreciation and amortization                                   186             165
          Cash used for store restructuring and other charges             (24)            (24)
          Increase in inventories                                        (909)           (517)
          Increase in accounts payable                                    993             666
          Increase in accounts receivable                                 (49)            (49)
          Deferred income taxes and taxes payable                          (8)             53
          (Decrease) increase in other long-term liabilities              (17)              3
          Changes in certain assets and liabilities                       (12)            (32)
                                                                        -----           -----
     Net cash provided by operating activities                            227             312
                                                                        -----           -----
CASH FLOW FROM INVESTING ACTIVITIES
     Acquisition of leases                                                (76)              -
     Proceeds from divestitures                                             -              87
     Increase in property held for sale or financing and other             (6)             (2)
     Capital expenditures                                                (227)           (145)
     Other, net                                                             -              (5)
                                                                        -----           -----
     Net cash used for investing activities                              (309)            (65)
                                                                        -----           -----

CASH FLOW FROM FINANCING ACTIVITIES
     Change in common stock                                                18              39
     Payments on capital lease obligations                                (18)            (21)
     Payments on long-term debt                                            (9)            (30)
                                                                        -----           -----
     Net cash used for financing activities                                (9)            (12)
                                                                        -----           -----
Net (decrease) increase in cash and cash equivalents                      (91)            235
Cash and cash equivalents at beginning of period                          710             498
                                                                        -----           -----
Cash and cash equivalents at end of period                              $ 619           $ 733
                                                                        =====           =====
</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
     1998 Annual Report and Form 10-K filed for the fiscal year ended January
     27, 1999.

              Certain reclassifications of the January 27, 1999 and April 29,
     1998 financial statements have been made to conform to current year
     presentation.

2.   PRE-OPENING COSTS

              Beginning in fiscal 1999, Kmart is expensing pre-opening costs in
     the period in which they are incurred in conformity with Statement of
     Position 98-5, "Reporting on the Costs of Start-Up Activities". Prior to
     fiscal 1999, pre-opening costs were deferred and expensed in the month the
     store opened. The implementation of SOP 98-5 is not expected to have a
     material effect on the Company's financial position, results of operations
     or cash flows for fiscal 1999. However, since the Company generally opens
     new locations during the second half of the year, the change in accounting
     for pre-opening costs could have an effect on quarterly results.

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
     April 28, 1999, April 29, 1998 and January 27, 1999 were $407 million, $457
     million and $407 million lower than the amounts that would have been
     reported under the first-in, first-out (FIFO) method, respectively.

4.   LEASE ACQUISITIONS

              On February 25, 1999, the Company entered into an agreement with
     Caldor Corporation to purchase the operating leases, fixtures, and
     equipment of eleven Caldor stores. The Company acquired two additional
     Caldor locations in April 1999. In addition to assuming annual minimum
     operating lease obligations of approximately $8.5 million, the total
     acquisition premium paid for these locations was approximately $76 million.
     The lease acquisition premium will be amortized over the remaining term of
     the acquired leases. The Company expects to open these stores in the second
     half of 1999.

5.   OTHER COMMITMENTS AND CONTINGENCIES

     Lease Guarantees
     ----------------
              Kmart has outstanding guarantees for property leased by certain
     former subsidiaries as follows:

<TABLE>
<CAPTION>
                                    Present Value of          Gross
                                      Future Lease            Future
                                    Obligations @ 7%     Lease Obligation
                                    ----------------     ----------------
     <S>                                <C>                  <C>
     Borders Group                      $  106               $  191
     OfficeMax                             104                  152
     The Sports Authority                  230                  390
     Builders Square                       711                1,307
                                        ------               ------
     Total                              $1,151               $2,040
                                        ======               ======
</TABLE>





                                       6
<PAGE>   7


                                KMART CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                            -- CONTINUED (UNAUDITED)

OTHER COMMITMENT AND CONTINGENCIES (CON'T)

         The possibility of the Company having to honor its contingent
obligations is dependent upon the future operating results of the former
subsidiaries. Should a reserve be required, it would be recorded at the time the
obligation was determined to be both probable and estimable.

         Builders Square

         The Builders Square operations are now part of Hechinger Company
("Hechinger"), an affiliate of Leonard Green and Partners LP ("LGP"). Hechinger
operates in the highly competitive "do-it-yourself" marketplace.

         On February 22, 1999, in its first quarter 10-Q filing, Hechinger
indicated that it might not be in compliance with the EBITDA covenant contained
in its bank agreement for its second quarter, ended April 3,1999, and arranged
with its lenders for a temporary waiver. On March 18, 1999, Hechinger entered
into a new secured credit facility which replaced all existing credit
facilities. Kmart and LGP do not provide any guarantees under this new facility
as they had under a previous supplemental credit facility.

         On May 18, 1999, in its second quarter 10-Q filing, Hechinger indicated
that under the terms of certain sale-leaseback transactions, it is required to
maintain a net worth of $200 million. As of April 3, 1999, Hechinger's net worth
was a deficit of $65.9 million. In the event that Hechinger is unable to improve
its net worth to the required level, it could be required to repurchase
properties at a cost of approximately $42 million. To do so, Hechinger would
have to borrow additional funds under its secured credit facility or arrange
other permitted third party financing for such properties. Hechinger indicated
that there can be no assurance that it would be able to consummante any such
transactions, if necessary. The earliest Hechinger expects to be required to
repurchase the properties is February 2000.

         Hechinger's Amended and Restated Credit Agreement contains a Minimum
Excess Availability covenant which Hechinger has indicated it does not expect to
meet as of the beginning of July 1999. In addition, Hechinger does not expect to
meet certain financial performance covenants which become effective June 30,
1999. Should Hechinger not be in compliance with these covenants, it will not be
able to continue to borrow under the Amended and Restated Credit Agreement.
Without a waiver or amendment, Hechinger would need to seek alternative
financing. Hechinger indicated that there can be no assurance that it would be
able to obtain such a waiver, amendment or alternative financing.

         On May 14, 1999, Hechinger was scheduled to make a semi-annual interest
payment of $4.7 million on its 9.45% Senior Debentures. Hechinger elected to
defer this interest payment and use its 30 day grace period. If Hechinger does
not make the required interest payment by the end of the grace period, it will
be in default and the maturity date of the debentures may be accelerated. In
addition, a cross-default will occur under certain sale-leaseback transactions,
and a default may occur under other contracts to which Hechinger is a party,
which in turn may result in a default under the Amended and Restated Credit
Agreement. Although Hechinger intends to seek waivers of all defaults, it
indicated that there can be no assurance that it will be able to obtain such
waivers.

         The Sports Authority

         On October 6, 1998, The Sports Authority ("TSA") announced that it
would take a $55 million after-tax charge, as a result of store closings,
inventory writedowns and other charges and costs, and that operating results for
the third quarter of 1998 would be weaker than expected. In October 1998, TSA
announced that it had amended certain aspects of its bank credit agreement,
including modifying certain financial covenants in light of the restructuring
charge. Pursuant to that amendment, TSA also granted its bank lenders a security
interest in its inventory and certain accounts receivable. On December 9, 1998,
in its third quarter 10-Q filing, TSA noted that its ability to satisfy ongoing
working capital and capital expenditure requirements would depend on the
successful negotiation of a new credit facility prior to the expiration of its
bank credit agreement in April 1999. On April 13, 1999, TSA entered into a new
credit facility.



                                       7
<PAGE>   8




                                KMART CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                            -- CONTINUED (UNAUDITED)

OTHER COMMITMENT AND CONTINGENCIES (CON'T)

         The Sports Authority (con't)

         Kmart's rights and obligations with respect to its guarantee of TSA
leases are governed by a Lease Guaranty, Indemnification and Reimbursement
Agreement dated as of November 23, 1994 (the "LGIRA"). Kmart and TSA are
presently in discussions to amend and restate the LGIRA, the terms of which have
not been finalized.

Other
-----

         There are various claims, lawsuits, and pending actions against Kmart
incident to its operations. It is the opinion of the Company's management that
the ultimate resolution of these matters will not have a material adverse effect
on Kmart's liquidity, financial position or results of operations.


















                                       8
<PAGE>   9

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)          APRIL 28,           APRIL 29,           ALL STORES          COMPARABLE STORES
                               1999                1998
                        ------------------   -----------------    ---------------       ------------------

<S>                     <C>                  <C>                          <C>                   <C>
SALES                   $            8,144   $           7,515            8.4                   6.5
                        ==================   =================

OPERATING INCOME        $              186   $             158
                        ==================   =================
</TABLE>


         SALES and comparable store sales increased 8.4% and 6.5%, respectively
for the 13 weeks ended April 28, 1999. The increases were primarily due to:
improved merchandise assortments including exclusive private label lines such as
Martha Stewart Everyday, Route 66 apparel and accessories, as well as Jaclyn
Smith and Kathy Ireland ladies apparel; continued roll out of the Big Kmart
format, with 132 store conversions during the quarter; and continued execution
of the Company's competitive pricing strategy. Divisions showing particular
strength for the quarter included consumables and edibles, pharmacy, housewares
and home decor, home appliances and electronics and ladies apparel. The Company
closed 12 stores and opened 2 stores during the first quarter.


         GROSS MARGIN, as a percentage of sales, was 21.2% and 21.4% for the 13
weeks ended April 28, 1999 and April 29, 1998, 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 margin improvements resulting from
refined merchandise assortments, increased import activity and a higher mix of
private label goods.


         SELLING, GENERAL AND ADMINISTRATIVE ("SG&A") EXPENSES, as a percentage
of sales, were 18.9% and 19.3%, for the 13 weeks ended April 28, 1999, and April
29, 1998, respectively. The 40 basis point decrease resulted primarily from
increased expense leverage given additional sales volume, partially offset by
incremental costs associated with new stores opened during 1998 and promotional
activities associated with key product offerings.


         OPERATING INCOME for the 13 weeks ended April 28, 1999 was $186
million, or 2.3% of sales, as compared to operating income of $158 million, or
2.1% of sales, for the same period of the prior year. This increase was the
result of increased sales volumes and the leveraging of SG&A expenses.


         NET INTEREST EXPENSE for the 13 weeks ended April 28, 1999 was $66
million as compared to $74 million for the same period of the prior year. Net
interest expense decreased as a result of overall lower levels of borrowings
resulting from scheduled repayments and repurchases of existing debt. See
"Liquidity and Financial Condition".






                                       9
<PAGE>   10


                                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 $4,116, $4,333 and $4,139 million at April 28, 1999, April 29, 1998,
and January 27, 1999, respectively. Working capital fluctuates in relation to
profitability, seasonal inventory levels net of trade accounts payable and the
level of store openings and closings. No borrowings were outstanding under the
Company's $2.5 billion Revolving Credit Agreement ("Revolver") during the first
quarter of 1999 or 1998.

         Net cash provided by operating activities for the 13 weeks ended April
28, 1999 was $227 million as compared to $312 million for the same period in
1998. The decrease in cash provided by operating activities was primarily the
result of increased net inventory resulting from the new stores opened during
1998, the launch of several key merchandise programs and increased import
activity.

         Net cash used for investing activities was $309 million for the 13
weeks ended April 28, 1999 compared to $65 million for the same period in 1998.
The increase in cash used for investing activities was primarily the result of
increased capital expenditures related to the Big Kmart rollout, new stores,
expansion of existing stores and the acquisition of thirteen Caldor leases. The
prior year's investing activities were also partially offset by the proceeds
received from the divestiture of Kmart Canada.

         Net cash used for financing activities was $9 million for the 13 weeks
ended April 28, 1999 compared to $12 million for the same period in 1998. The
decrease in cash used for financing activities was primarily a result of lower
payments on long-term debt due to bonds repurchased in the prior year.

         Management believes that its current financing arrangements will be
sufficient to meet the Company's liquidity needs for operations and capital
demands.

YEAR 2000

         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 phases I, II and III. Phase IV has commenced
and is planned to be completed by the end of the third quarter of 1999.
Substantially all business critical applications have been returned to
production. The non-information technology equipment at a significant number of
the Company's operating locations is already fully Year 2000 compliant.
Non-information technology equipment at the remainder of the Company's locations
is expected to be Year 2000 compliant by the end of the third quarter 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 99% of significant merchandise vendors have responded, most
indicating 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,
substitutes for many of the goods the Company sells and 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.
In addition, the Company is currently conducting integration testing with third
parties' systems with which the Company's systems interface. The Company
anticipates that such testing will be substantially completed by the end of the
third quarter of 1999.





                                       10
<PAGE>   11

                                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. 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 Kmart's customers, the Company is 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, $46 million incurred
in 1998, and $8 million incurred year-to-date. Year 2000 Compliance Program
costs 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 which 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".

         The Year 2000 statement set forth below is a Year 2000 Readiness
Disclosure, pursuant to the Year 2000 Information and Readiness Disclosure Act,
15 U.S.C. Section 1 note. 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.

OTHER MATTERS

         In the first quarter of fiscal 1999, the Company repurchased 62,300
shares of common stock at a cost of approximately $1 million, thereby completing
a year-long program to repurchase an aggregate of 2,000,000 shares of the
Company's common stock to fund certain employee benefit plans.

         Kmart has guaranteed leases for properties operated by certain former
subsidiaries including Borders Group, Inc., OfficeMax, Inc., The Sports
Authority, Inc. and Builders Square, Inc. The present value of the lease
obligations guaranteed by Kmart is approximately $1.2 billion. The possibility
of the Company having to honor its contingent obligations is dependent upon the
future operating results of the former subsidiaries. (See Note 5 of the Notes to
Consolidated Financial Statements)





                                       11
<PAGE>   12
                                KMART CORPORATION
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF OPERATIONS AND
                        FINANCIAL CONDITION -- CONTINUED

OTHER MATTERS (CON'T)

         There are various claims, lawsuits, and pending actions against Kmart
incident to its operations. It is the opinion of the Company's management that
the ultimate resolution of these matters will not have a material adverse effect
on Kmart's liquidity, financial position or results of operations.

SUBSEQUENT EVENT

         On May 18, 1999, the board of directors approved a common stock
repurchase program to acquire up to $1 billion of the Company's common shares
over a period of up to three years.

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. Statements,
other than those based on historical facts, including the discussion of
management's 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.












                                       12
<PAGE>   13

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

(b)      Reports on Form 8-K: No reports were filed on Form 8-K by the
         Registrant during the 13 weeks ended April 28, 1999.











                                       13
<PAGE>   14


                                   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:            May 24, 1999
                                                       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)







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<PAGE>   15
                                 EXHIBIT INDEX

Exhibit
Number                         Description
----------                     -----------
Exhibit 11                     Information on Computation of Per Share Earnings
Exhibit 27                     Financial Data Schedule