<PAGE>   1
                                                                    EXHIBIT 99.1

                         [KMART CORPORATION LETTERHEAD]

                                  NEWS RELEASE

                            RELEASE DATE
                                November 10, 1999

                            CONTACTS
                                Robert M. Burton
                                Divisional Vice President, Investor Relations
                                (248) 643-1040

                                Shawn M. Kahle
                                Vice President, Corporate Affairs
                                (248) 637-4201

FOR IMMEDIATE RELEASE

KMART CORPORATION REPORTS 13 PERCENT INCREASE
IN EARNINGS PER SHARE IN 1999 THIRD QUARTER

EARNINGS FROM CONTINUING OPERATIONS UP 37.1 PERCENT YEAR-TO-DATE

TROY, Mich., November 10, 1999--Kmart Corporation (NYSE:KM) today reported a 13
percent increase in net income to $43 million, or $0.09 basic earnings per
share, for the 13 weeks ended October 27, 1999, compared with net income of $38
million, or $0.08 basic earnings per share for the 13 weeks ended October 28,
1998.

"While our third quarter performance was softer than planned, the results extend
our string of improved operating performance to 14 consecutive quarters, " said
Floyd Hall, Chairman, President and CEO.

Total consolidated sales in the third quarter of 1999 were $8.057 billion, an
increase of 5.4% from $7.642 billion for the third quarter of 1998. Comparable
sales for the quarter increased 3.2%. The gross margin rate for the quarter was
21.6% of sales as compared with 22.1% last year. Selling, general and
administrative (SG&A) expenses for the quarter were $1.581 billion compared with
$1.540 billion for 1998, resulting in a SG&A to sales ratio of 19.6% for 1999
versus 20.1% for 1998.

Sales from consolidated operations for the first nine months of 1999 were
$24.958 billion, up 7.2% from $23.273 billion for the first nine months of
fiscal 1998. On a comparable store basis, consolidated sales rose 5.2% for the
same period. Income from continuing operations was $244 million, or $0.49 per
share, for the first nine months of 1999 as compared with net income before
non-recurring items of $178 million, or $0.36 per share in the first nine months
of 1998.

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As previously reported, net income for the nine months of 1999 included a
non-recurring, non-cash charge for discontinued operations of $230 million after
tax, relating to the disposition of certain Builders Square operating leases.
Net income for the second quarter 1998 included a non-recurring charge of $13
million after tax, relating to a Voluntary Early Retirement Program (VERP) in
the Company's distribution centers. Including the non-recurring charges, net
income for the first nine months of 1999 was $14 million as compared with net
income of $165 million for the comparable 1998 period.

Under FAS 128, preferred securities are not included in the calculation of
diluted earnings per share for the third quarter of either 1999 or 1998 due to
their anti-dilutive effect. However, consistent with disclosure required by the
Securities and Exchange Commission, if such securities were included in the
calculation, diluted earnings per share would have been $0.10 and $0.09 for the
third quarters of 1999 and 1998, respectively.

Under the Company's previously-announced share repurchase plan initiated in June
1999, at the close of the third quarter Kmart had acquired 10.1 million common
shares through open market purchases for a total of $126 million.

Kmart Corporation serves America with 2,159 Kmart retail outlets. Kmart
Corporation common stock is listed on the New York, Pacific, and Chicago Stock
Exchanges.

<PAGE>   3


                                KMART CORPORATION
                        CONSOLIDATED STATEMENTS OF INCOME

<TABLE>
<CAPTION>
(Dollars in millions, except per share data)                                                 13 Weeks         13 Weeks
                                                                                              Ended            Ended
                                                                                             10/27/99         10/28/98
                                                                                         ----------------------------------
<S>                                                                                      <C>                 <C>
Sales                                                                                    $          8,057    $       7,642
Cost of sales, buying and occupancy                                                                 6,317            5,954
                                                                                         ----------------------------------
Gross margin                                                                                        1,740            1,688
Selling, general and administrative expenses                                                        1,581            1,540
                                                                                         ----------------------------------
Income before interest, income taxes and dividends on
 convertible preferred securities of subsidiary                                                       159              148
Interest expense, net                                                                                  76               76
Income tax provision                                                                                   27               21
Dividends on convertible preferred securities, net of income taxes                                     13               13
                                                                                         ----------------------------------
Net income                                                                               $             43    $          38
                                                                                         ==================================

Basic / diluted income per common share                                                  $           0.09    $        0.08
                                                                                         ==================================

Basic weighted average shares (millions)                                                            492.1            492.8
Diluted weighted average shares (millions)                                                          562.2            564.0
</TABLE>

    The effect of LIFO adjustments on the third quarter of fiscal 1999 results
    was a pre-tax credit of $13 million, compared to a pre-tax credit of $2
    million in 1998.
<PAGE>   4


                                KMART CORPORATION
                        CONSOLIDATED STATEMENTS OF INCOME

<TABLE>
<CAPTION>
(Dollars in millions, except per share data)                                                 39 Weeks         39 Weeks
                                                                                              Ended            Ended
                                                                                             10/27/99         10/28/98
                                                                                         ----------------------------------
<S>                                                                                      <C>                <C>
Sales                                                                                    $         24,958   $       23,273
Cost of sales, buying and occupancy                                                                19,569           18,198
                                                                                         ----------------------------------
Gross margin                                                                                        5,389            5,075
Selling, general and administrative expenses                                                        4,762            4,550
Voluntary early retirement program                                                                      -               19
                                                                                         ----------------------------------
Income before interest, income taxes and dividends on
 convertible preferred securities of subsidiary                                                       627              506
Interest expense, net                                                                                 206              220
Income tax provision                                                                                  139               83
Dividends on convertible preferred securities, net of income taxes                                     38               38
                                                                                         ----------------------------------
Income from continuing operations                                                                     244              165
Discontinued operations, net of tax:  Provision for lease obligations resulting
from guarantee of previously owned Builders Square locations                                         (230)               -
                                                                                         ----------------------------------
Net income                                                                               $             14   $          165
                                                                                         ==================================

Basic / diluted earnings per common share:
Income from continuing operations                                                        $           0.49   $         0.34
Discontinued operations                                                                             (0.46)               -
                                                                                         ----------------------------------
Net income (loss)                                                                        $           0.03   $         0.34
                                                                                         ==================================

Basic weighted average shares (millions)                                                            493.8            491.7
Diluted weighted average shares (millions)                                                          566.5            564.8
</TABLE>

    The effect of LIFO adjustments on the year to date fiscal 1999 results was a
    pre-tax credit of $10 million, compared with a charge of $8 million in 1998.

<PAGE>   5


                                KMART CORPORATION
                           CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
(Dollars in millions)                                                                        10/27/99          10/28/98
                                                                                         ----------------------------------
<S>                                                                                      <C>                 <C>
ASSETS
Current Assets:
Cash and cash equivalents                                                                $            345    $         350
Merchandise inventories                                                                             8,486            8,060
Other current assets                                                                                  865              844
                                                                                         ----------------------------------
Total current assets                                                                                9,696            9,254

Property and equipment, net                                                                         6,313            5,852
Other assets and deferred charges                                                                     489              443
                                                                                         ----------------------------------
TOTAL ASSETS                                                                             $         16,498    $      15,549
                                                                                         ==================================

LIABILITIES AND EQUITY
Current Liabilities:
Long-term debt due within one year                                                       $             74    $          60
Trade accounts payable                                                                              3,119            3,019
Accrued payroll and other liabilities                                                               1,324            1,242
Taxes other than income taxes                                                                         252              240
                                                                                         ----------------------------------
Total current liabilities                                                                           4,769            4,561

Long-term debt and notes payable                                                                    2,730            2,313
Capital lease obligations                                                                           1,031            1,114
Other long-term liabilities                                                                         1,057              928
Convertible preferred securities, net                                                                 985              983
Common stock                                                                                          487              493
Capital in excess of par value                                                                      1,607            1,654
Retained earnings                                                                                   3,832            3,503
                                                                                         ----------------------------------
TOTAL LIABILITIES AND EQUITY                                                             $         16,498    $      15,549
                                                                                         ==================================
</TABLE>

<PAGE>   6


                                KMART CORPORATION
                      CONSOLIDATED STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>
(Dollars in millions)                                                                        39 Weeks         39 Weeks
                                                                                              Ended            Ended
                                                                                             10/27/99         10/28/98
                                                                                         ----------------------------------
<S>                                                                                      <C>                  <C>
CASH FLOW FROM OPERATING ACTIVITIES
      Income from continuing operations                                                  $            244     $        165
      Adjustments to reconcile income from continuing operations to net cash
           used for operating activities:
           Depreciation and amortization                                                              568              498
           Cash used for store restructuring and other charges                                       (111)             (95)
           Increase in inventories                                                                 (1,950)          (1,693)
           Increase in accounts payable                                                             1,072            1,096
           Increase in accounts receivable                                                           (181)            (176)
           Increase in prepaids                                                                       (35)             (69)
           Increase in sales tax payable                                                               19               30
           Deferred income taxes and taxes payable                                                     73              166
           Decrease in other long-term liabilities                                                    (23)              (2)
           Changes in certain assets and liabilities                                                  (14)               9
           Voluntary early retirement program                                                           -               19
                                                                                         ----------------------------------
Net cash used for operating activities                                                               (338)             (52)
                                                                                         ----------------------------------

CASH FLOW FROM INVESTING ACTIVITIES
      Acquisition of Caldor leases                                                                    (86)               -
      Proceeds from sale of Canadian operations                                                         -               87
      Capital expenditures                                                                           (997)            (722)
                                                                                         ----------------------------------
Net cash used for investing activities                                                             (1,083)            (635)
                                                                                         ----------------------------------

CASH FLOW FROM FINANCING ACTIVITIES
      Proceeds from issuance of long-term debt                                                      1,250              750
      Payments on long-term debt                                                                      (61)            (180)
      Purchase of common shares                                                                      (117)             (30)
      Issuance of common shares                                                                        44               64
      Payments on capital lease obligations                                                           (60)             (65)
                                                                                         ----------------------------------
Net cash provided by financing activities                                                           1,056              539
                                                                                         ----------------------------------

Net decrease in cash and cash equivalents                                                            (365)            (148)
Cash and cash equivalents at beginning of period                                                      710              498
                                                                                         ----------------------------------
Cash and cash equivalents at end of period                                               $            345     $        350
                                                                                         ==================================
</TABLE>