<PAGE>   1
                                                         Registration No. 333-- 

                     SECURITIES AND EXCHANGE COMMISSION

                           Washington, D.C.  20549


                                  FORM S-8
                           REGISTRATION STATEMENT
                                    Under
                         The Securities Act of 1933


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

                              KMART CORPORATION

            (Exact number of issuer as specified in its charter)



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


                3100 West Big Beaver Road, Troy, Michigan 48084
              (Address of Principal Executive Offices)  (Zip Code)


                              Hall Stock Option

                           (Full title of the plans)


                                 A. N. Palizzi
                  Executive Vice President and General Counsel
                               Kmart Corporation
                           3100 West Big Beaver Road
                              Troy, Michigan 48084
                    (Name and Address of agent for service)
          Telephone number, including area code, of agent of service:
                                  248-643-1000

                          Copies of Communications to:
                              Verne C. Hampton II
                            Dickinson Wright PLLC
                            500 Woodward, Suite 4000
                            Detroit, Michigan 48226

                 Approximate date of proposed public offering:
 As soon as practicable after the effective date of this Registration Statement

                        CALCULATION OF REGISTRATION FEE




<TABLE>
<CAPTION>
                                              Proposed Maximum           Proposed
Title of Securities      Amount to be         Offering Price Per      Maximum Aggregate          Amount of
to be Registered         Registered                Share*              Offering Price         Registration Fee
<S>                      <C>                  <C>                      <C>                   <C>     
Common Stock ($1          950,000              $18 1/8                  $17,218,750           $5,080         
par value)......          shs.

</TABLE>

*Based upon the market price on August 12, 1998

<PAGE>   2

                                    PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT


                INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE
ITEM 3.

Kmart Corporation (the "Company) hereby incorporates by reference in this
Registration Statement the following documents previously filed with the
Securities and Exchange Commission (the "Commission") under the Securities
Exchange Act of 1934, as amended (the "Exchange Act"):

     1. The Company's Annual Report on Form 10-K for the year ended January
28, 1998.

     2. The Company's Quarterly Report on Form 10-Q for the quarter ended
April 29, 1998.

     3. The description of the Common Stock, $1.00 par value, of the
Company set forth in the Prospectus of the Company dated June 6, 1996
which was part of Amendment No. 1 to Registration Statement No.
33-64905.

All documents subsequently filed with the Commission by the Company pursuant
to Sections 13(a), 13(c), 14 and 15(d) of the Exchange Act prior to the
filing of a post-effective amendment which indicates that all securities
offered hereby have been sold or which deregisters all securities then
remaining unsold shall be deemed to be incorporated herein by reference and
to be a part hereof from the dates of filing of such documents.

ITEM 4.                DESCRIPTION OF SECURITIES

Not Applicable.

ITEM 5.          INTEREST OF NAMED EXPERTS AND COUNSEL

Not Applicable.

ITEM 6.          INDEMNIFICATION OF DIRECTORS AND OFFICERS

The Company's Bylaws and the Michigan Business Corporation Act permit the
Company's officers and directors to be indemnified under certain
circumstances for expenses and in some instances, for judgments, fines or
amounts paid in settlement of civil, criminal, administrative and
investigative suits or proceedings, including those involving alleged
violations of the Securities Act of 1933, as amended (the "Act").  In
addition, the Company maintains directors' and officers' liability insurance
which, under certain circumstances, would cover alleged violations of the
Act.  Insofar as indemnification for liabilities arising under the Act may
be permitted to officers and directors pursuant to the foregoing provisions,
the Company has been informed that, in the opinion of the Securities and
Exchange Commission, such indemnification is against public policy as
expressed in the Act and is, therefore, unenforceable.  Therefore in the
event that a claim for such indemnification is asserted by any officer or
director, the Company (except insofar as such claim seeks reimbursement by
the Company of the expenses paid or incurred by an officer or director in
the successful defense of any action, suit or proceeding) will, unless the
matter has heretofore been adjudicated by precedent deemed by the Company to
be controlling, submit to a court of appropriate jurisdiction the question
of whether or not the indemnification by it is against public policy as
expressed in the Act and will be governed by the final adjudication of such
issue.

ITEM 7. EXEMPTION FROM REGISTRATION CLAIMED

Not Applicable

<PAGE>   3

ITEM 8. EXHIBITS

The following exhibits are filed herewith:



              Exhibit
              Number                     Exhibit
              -------                    -------


                5                  Opinion and consent of Dickinson Wright PLLC

               24                  Consent of PricewaterhouseCoopers LLP

               28(a)               Hall Option Agreement


ITEM 9. UNDERTAKINGS

The undersigned Company hereby undertakes:  1.  To file, during any period
in which offers or sales are being made, a post-effective amendment to this
Registration Statement:  (i) to include any Prospectus required by Section
10(a) (3) of the Securities Act of 1933; (ii) to reflect in the Prospectus
any facts or events arising after the effective date of the Registration
Statement (or the most recent post-effective amendment thereof) which,
individually or in the aggregate, represent a fundamental change in the
information set forth in the Registration Statement; (iii) to include any
material information with respect to the plan of distribution not previously
disclosed in the Registration Statement or any material change to such
information in the Registration Statement; provided, however, that
paragraphs (a)(1)(i) and (a)(1)(ii) do not apply if the information required
to be included in a post-effective amendment by those paragraphs is
contained in periodic reports filed by the Company pursuant to Section 13 or
Section 15(d) of the Securities Exchange Act of 1934 that are incorporated
by reference in the Registration Statement.  (2)  That, for purposes of
determining any liability under the Securities Act of 1933, each such
post-effective amendment shall be deemed to be a new Registration Statement
relating to the securities offered therein, and the offering of such
securities at that time shall be deemed to be the initial bona fide offering
thereof.  (3)  To remove from registration by means of a  post-effective
amendment any of the securities being registered which remain unsold at the
termination of the offering.

The undersigned Company hereby undertakes that, for purposes of determining
any liability under the Securities Act of 1933, each filing of the Company's
annual report pursuant to Section 13(a) or Section 15(d) of the Securities
Exchange Act of 1934 that is incorporated by reference in the Registration
Statement shall be deemed to be a new Registration Statement relating to the
securities offered therein, and the offering of such securities at that time
shall be deemed to be the initial bona fide offering thereof.

Insofar as indemnification for liabilities arising under the Securities Act
of 1933 may be permitted to directors, officers and controlling persons of
the Company pursuant to the foregoing provisions, or otherwise, the Company
has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the
Act and is, therefore, unenforceable.  In the event that a claim for
indemnification against such liabilities (other than the payment by the
Company of expenses incurred or paid by a director, officer or controlling
person of the Company, in the successful defense of any action, suit or
proceeding) is asserted by such director, officer or controlling person in
connection with the securities being registered, the Company will, unless in
the opinion of its counsel the matter has been settled by controlling
precedent, submit to a court of appropriate jurisdiction the question of
whether or not such indemnification by it is against public policy as
expressed in the Act and will be governed by the final adjudication of such
issue.

<PAGE>   4


                                   SIGNATURES


     Pursuant to the requirements of the Securities Act of 1933, the
Registrant certifies that it has reasonable grounds to believe that it meets
all of the requirements for filing on Form S-8 and has duly caused this
Registration Statement or amendment thereto to be signed on its behalf by
the undersigned, thereunto duly authorized, in the City of Troy and State of
Michigan on August 12, 1998.


                              KMART CORPORATION


                                     By  /s/ Floyd Hall
                                        -------------------
                                        (Floyd Hall)
                                        Chairman of the Board, President
                                        and Chief Executive Officer


     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement or amendment thereto has been signed below by the
following persons in the capacities indicated on August 12, 1998.


<TABLE>
<CAPTION>

SIGNATURE                               TITLE                              SIGNATURE                    TITLE
<S>                               <C>                                 <C>                             <C>               
/s/ Floyd Hall                     Chairman of the Board,                                                       
-----------------------------      President and Chief Executive                                                
(Floyd Hall)                       Officer (Principal Executive                                                 
                                   Officer) and Director                                                        
                                                                                                                
/s/ Martin E. Welch III            Senior Vice President and Chief                                                      
-----------------------------      Financial Officer (Principal                                                 
(Martin E. Welch III)              Financial Officer)                                                           
                                                 
/s/ William C. Najdecki            Vice President, Controller          
-----------------------------      (Principal Accounting Officer)      
(William C. Najdecki)                                                  

                                   Director                            /s/ Joseph P. Flannery          Director         
-----------------------------                                          ----------------------------- 
(James B. Adamson)                                                     (Joseph P. Flannery)    

/s/ Lilyan H. Affinito             Director                            /s/ Robert Kennedy              Director 
-----------------------------                                          -----------------------------                 
(Lilyan H. Affinito)                                                   (Robert Kennedy)                         
                                                                                                                
/s/ Stephen F. Bollenbach          Director                            /s/ J. Richard Munro            Director 
-----------------------------                                          -----------------------------                 
(Stephen F. Bollenbach)                                                (J. Richard Munro)                       
                                                                                                                
/s/ Joseph A. Califano, Jr.        Director                            /s/ Robin B. Smith              Director 
-----------------------------                                          -----------------------------           
(Joseph A. Califano, Jr.)                                              (Robin B. Smith)                         
                                                                                                                
/s/ Richard G. Cline               Director                                                                     
-----------------------------                                          /s/ James O. Welch, Jr.         Director 
(Richard G. Cline)                                                     -----------------------------           
                                                                       (James O. Welch, Jr.)                    
                                                                       
/s/ Willie D. Davis                Director                             /s/ William P. Weber           Director 
-----------------------------                                           ----------------------------           
(Willie D. Davis)                                                       (William P. Weber)
                                                                       

</TABLE>
<PAGE>   5



                                EXHIBIT INDEX




Exhibit
Number                          Exhibit
-------                         -------

  5                     Opinion and consent of Dickinson Wright PLLC

 24                     Consent of PricewaterhouseCoopers LLP

 28(a)                  Hall Option Agreement
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 14713}]
{"company-data": {"conformed-name": "KMART CORP", "cik": "0000056824", "assigned-sic": "5331", "irs-number": "380729500", "state-of-incorporation": "MI", "fiscal-year-end": "0129"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-61351", "film-number": "98685573"}, "business-address": {"street1": "3100 W BIG BEAVER RD", "city": "TROY", "state": "MI", "zip": "48084", "phone": "8106431000"}, "mail-address": {"street1": "3100 W  BIG BEAVER ROAD", "city": "TROY", "state": "MI", "zip": "48084"}, "former-company": {"former-conformed-name": "KRESGE S S CO", "date-changed": "19770921"}}
1
                                                         Registration No. 333-- 

                     SECURITIES AND EXCHANGE COMMISSION

                           Washington, D.C.  20549

                                  FORM S-8
                           REGISTRATION STATEMENT
                                    Under
                         The Securities Act of 1933

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

                              KMART CORPORATION

            (Exact number of issuer as specified in its charter)

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

                3100 West Big Beaver Road, Troy, Michigan 48084
              (Address of Principal Executive Offices)  (Zip Code)

                              Hall Stock Option

                           (Full title of the plans)

                                 A. N. Palizzi
                  Executive Vice President and General Counsel
                               Kmart Corporation
                           3100 West Big Beaver Road
                              Troy, Michigan 48084
                    (Name and Address of agent for service)
          Telephone number, including area code, of agent of service:
                                  248-643-1000

                          Copies of Communications to:
                              Verne C. Hampton II
                            Dickinson Wright PLLC
                            500 Woodward, Suite 4000
                            Detroit, Michigan 48226

                 Approximate date of proposed public offering:
 As soon as practicable after the effective date of this Registration Statement

                        CALCULATION OF REGISTRATION FEE
Proposed Maximum           Proposed
Title of Securities      Amount to be         Offering Price Per      Maximum Aggregate          Amount of
to be Registered         Registered                Share*              Offering Price         Registration Fee
Common Stock ($1          950,000              $18 1/8                  $17,218,750           $5,080         
par value)......          shs.
*Based upon the market price on August 12, 1998
2

                                    PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

                INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE
ITEM 3.

Kmart Corporation (the "Company) hereby incorporates by reference in this
Registration Statement the following documents previously filed with the
Securities and Exchange Commission (the "Commission") under the Securities
Exchange Act of 1934, as amended (the "Exchange Act"):

     1. The Company's Annual Report on Form 10-K for the year ended January
28, 1998.

     2. The Company's Quarterly Report on Form 10-Q for the quarter ended
April 29, 1998.

     3. The description of the Common Stock, $1.00 par value, of the
Company set forth in the Prospectus of the Company dated June 6, 1996
which was part of Amendment No. 1 to Registration Statement No.
33-64905.

All documents subsequently filed with the Commission by the Company pursuant
to Sections 13(a), 13(c), 14 and 15(d) of the Exchange Act prior to the
filing of a post-effective amendment which indicates that all securities
offered hereby have been sold or which deregisters all securities then
remaining unsold shall be deemed to be incorporated herein by reference and
to be a part hereof from the dates of filing of such documents.

ITEM 4.                DESCRIPTION OF SECURITIES

Not Applicable.

ITEM 5.          INTEREST OF NAMED EXPERTS AND COUNSEL

Not Applicable.

ITEM 6.          INDEMNIFICATION OF DIRECTORS AND OFFICERS

The Company's Bylaws and the Michigan Business Corporation Act permit the
Company's officers and directors to be indemnified under certain
circumstances for expenses and in some instances, for judgments, fines or
amounts paid in settlement of civil, criminal, administrative and
investigative suits or proceedings, including those involving alleged
violations of the Securities Act of 1933, as amended (the "Act").  In
addition, the Company maintains directors' and officers' liability insurance
which, under certain circumstances, would cover alleged violations of the
Act.  Insofar as indemnification for liabilities arising under the Act may
be permitted to officers and directors pursuant to the foregoing provisions,
the Company has been informed that, in the opinion of the Securities and
Exchange Commission, such indemnification is against public policy as
expressed in the Act and is, therefore, unenforceable.  Therefore in the
event that a claim for such indemnification is asserted by any officer or
director, the Company (except insofar as such claim seeks reimbursement by
the Company of the expenses paid or incurred by an officer or director in
the successful defense of any action, suit or proceeding) will, unless the
matter has heretofore been adjudicated by precedent deemed by the Company to
be controlling, submit to a court of appropriate jurisdiction the question
of whether or not the indemnification by it is against public policy as
expressed in the Act and will be governed by the final adjudication of such
issue.

ITEM 7. EXEMPTION FROM REGISTRATION CLAIMED

Not Applicable
3

ITEM 8. EXHIBITS

The following exhibits are filed herewith:

              Exhibit
              Number                     Exhibit
              -------                    -------

                5                  Opinion and consent of Dickinson Wright PLLC

               24                  Consent of PricewaterhouseCoopers LLP

               28(a)               Hall Option Agreement

ITEM 9. UNDERTAKINGS

The undersigned Company hereby undertakes:  1.  To file, during any period
in which offers or sales are being made, a post-effective amendment to this
Registration Statement:  (i) to include any Prospectus required by Section
10(a) (3) of the Securities Act of 1933; (ii) to reflect in the Prospectus
any facts or events arising after the effective date of the Registration
Statement (or the most recent post-effective amendment thereof) which,
individually or in the aggregate, represent a fundamental change in the
information set forth in the Registration Statement; (iii) to include any
material information with respect to the plan of distribution not previously
disclosed in the Registration Statement or any material change to such
information in the Registration Statement; provided, however, that
paragraphs (a)(1)(i) and (a)(1)(ii) do not apply if the information required
to be included in a post-effective amendment by those paragraphs is
contained in periodic reports filed by the Company pursuant to Section 13 or
Section 15(d) of the Securities Exchange Act of 1934 that are incorporated
by reference in the Registration Statement.  (2)  That, for purposes of
determining any liability under the Securities Act of 1933, each such
post-effective amendment shall be deemed to be a new Registration Statement
relating to the securities offered therein, and the offering of such
securities at that time shall be deemed to be the initial bona fide offering
thereof.  (3)  To remove from registration by means of a  post-effective
amendment any of the securities being registered which remain unsold at the
termination of the offering.

The undersigned Company hereby undertakes that, for purposes of determining
any liability under the Securities Act of 1933, each filing of the Company's
annual report pursuant to Section 13(a) or Section 15(d) of the Securities
Exchange Act of 1934 that is incorporated by reference in the Registration
Statement shall be deemed to be a new Registration Statement relating to the
securities offered therein, and the offering of such securities at that time
shall be deemed to be the initial bona fide offering thereof.

Insofar as indemnification for liabilities arising under the Securities Act
of 1933 may be permitted to directors, officers and controlling persons of
the Company pursuant to the foregoing provisions, or otherwise, the Company
has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the
Act and is, therefore, unenforceable.  In the event that a claim for
indemnification against such liabilities (other than the payment by the
Company of expenses incurred or paid by a director, officer or controlling
person of the Company, in the successful defense of any action, suit or
proceeding) is asserted by such director, officer or controlling person in
connection with the securities being registered, the Company will, unless in
the opinion of its counsel the matter has been settled by controlling
precedent, submit to a court of appropriate jurisdiction the question of
whether or not such indemnification by it is against public policy as
expressed in the Act and will be governed by the final adjudication of such
issue.
4

                                   SIGNATURES

     Pursuant to the requirements of the Securities Act of 1933, the
Registrant certifies that it has reasonable grounds to believe that it meets
all of the requirements for filing on Form S-8 and has duly caused this
Registration Statement or amendment thereto to be signed on its behalf by
the undersigned, thereunto duly authorized, in the City of Troy and State of
Michigan on August 12, 1998.

                              KMART CORPORATION

                                     By  /s/ Floyd Hall
                                        -------------------
                                        (Floyd Hall)
                                        Chairman of the Board, President
                                        and Chief Executive Officer

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement or amendment thereto has been signed below by the
following persons in the capacities indicated on August 12, 1998.
SIGNATURE                               TITLE                              SIGNATURE                    TITLE
/s/ Floyd Hall                     Chairman of the Board,                                                       
-----------------------------      President and Chief Executive                                                
(Floyd Hall)                       Officer (Principal Executive                                                 
                                   Officer) and Director                                                        
                                                                                                                
/s/ Martin E. Welch III            Senior Vice President and Chief                                                      
-----------------------------      Financial Officer (Principal                                                 
(Martin E. Welch III)              Financial Officer)                                                           
                                                 
/s/ William C. Najdecki            Vice President, Controller          
-----------------------------      (Principal Accounting Officer)      
(William C. Najdecki)                                                  

                                   Director                            /s/ Joseph P. Flannery          Director         
-----------------------------                                          ----------------------------- 
(James B. Adamson)                                                     (Joseph P. Flannery)    

/s/ Lilyan H. Affinito             Director                            /s/ Robert Kennedy              Director 
-----------------------------                                          -----------------------------                 
(Lilyan H. Affinito)                                                   (Robert Kennedy)                         
                                                                                                                
/s/ Stephen F. Bollenbach          Director                            /s/ J. Richard Munro            Director 
-----------------------------                                          -----------------------------                 
(Stephen F. Bollenbach)                                                (J. Richard Munro)                       
                                                                                                                
/s/ Joseph A. Califano, Jr.        Director                            /s/ Robin B. Smith              Director 
-----------------------------                                          -----------------------------           
(Joseph A. Califano, Jr.)                                              (Robin B. Smith)                         
                                                                                                                
/s/ Richard G. Cline               Director                                                                     
-----------------------------                                          /s/ James O. Welch, Jr.         Director 
(Richard G. Cline)                                                     -----------------------------           
                                                                       (James O. Welch, Jr.)                    
                                                                       
/s/ Willie D. Davis                Director                             /s/ William P. Weber           Director 
-----------------------------                                           ----------------------------           
(Willie D. Davis)                                                       (William P. Weber)
5

                                EXHIBIT INDEX

Exhibit
Number                          Exhibit
-------                         -------

  5                     Opinion and consent of Dickinson Wright PLLC

 24                     Consent of PricewaterhouseCoopers LLP

 28(a)                  Hall Option Agreement