Ownership Submission
FORM 4
Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).
UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES

Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940
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(Print or Type Responses)
1. Name and Address of Reporting Person *
ESL INVESTMENTS INC
  2. Issuer Name and Ticker or Trading Symbol
Sears Holdings CORP [SHLD]
5. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
_____ Director __X__ 10% Owner
_____ Officer (give title below) _____ Other (specify below)
(Last)
(First)
(Middle)
200 GREENWICH AVENUE
3. Date of Earliest Transaction (Month/Day/Year)
04/29/2005
(Street)

GREENWICH, CT 06830
4. If Amendment, Date Original Filed(Month/Day/Year)
6. Individual or Joint/Group Filing(Check Applicable Line)
___ Form filed by One Reporting Person
_X_ Form filed by More than One Reporting Person
(City)
(State)
(Zip)
Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security
(Instr. 3)
2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code
(Instr. 8)
4. Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4 and 5)
5. Amount of Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 3 and 4)
6. Ownership Form: Direct (D) or Indirect (I)
(Instr. 4)
7. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V Amount (A) or (D) Price
Common Stock, par value $0.01 per share 04/29/2005   J(1)   201,413 A (1) 47,657,038 D (2)  
Common Stock, par value $0.01 per share 04/29/2005   J(1)   63,059 A (1) 16,819,887 D (3)  
Common Stock, par value $0.01 per share 04/29/2005   J(1)   264,472 A (1) 64,476,925 I (4) (12) (13) see footnote (4)
Common Stock, par value $0.01 per share 04/29/2005   J(1)   264,472 A (1) 64,815,911 I (5) (12) (13) see footnote (5)
Common Stock, par value $0.01 per share 04/29/2005   J(1)   264,472 A (1) 64,831,910 I (6) (12) (13) see footnote (6)
Common Stock, par value $0.01 per share               747 D (7)  
Common Stock, par value $0.01 per share               15,999 D (8)  
Common Stock, par value $0.01 per share               338,239 D (9)  
Common Stock, par value $0.01 per share               338,239 I (10) (12) (13) see footnote (10)
Common Stock, par value $0.01 per share               0 D (11)  

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 3)
2. Conversion or Exercise Price of Derivative Security 3. Transaction Date (Month/Day/Year) 3A. Deemed Execution Date, if any (Month/Day/Year) 4. Transaction Code
(Instr. 8)
5. Number of Derivative Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4, and 5)
6. Date Exercisable and Expiration Date
(Month/Day/Year)
7. Title and Amount of Underlying Securities
(Instr. 3 and 4)
8. Price of Derivative Security
(Instr. 5)
9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 4)
10. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 4)
11. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V (A) (D) Date Exercisable Expiration Date Title Amount or Number of Shares

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
ESL INVESTMENTS INC
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
ESL PARTNERS LP
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
ESL INSTITUTIONAL PARTNERS LP
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
ESL INVESTORS LLC
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
RBS INVESTMENT MANAGEMENT LLC
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
RBS PARTNERS L P /CT
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
ESL INVESTMENT MANAGEMENT LLC
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
CRK PARTNERS LLC
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
CRK PARTNERS II LP
200 GREENWICH AVENUE
GREENWICH, CT 06830
    X    
LAMPERT EDWARD S
200 GREENWICH AVENUE
GREENWICH, CT 06830
  X   X    

Signatures

 /s/ Robert Jackowitz, Treasurer (See signatures of other Reporting Persons as Exhibit 99.1)   05/03/2005
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 4(b)(v).
** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1) These shares of Common Stock, par value $0.01 per share of Sears Holdings Corporation ("Common Stock") were distributed by Kmart Holding Corporation on account of previously reported trade vendor/lease rejection claims (and participations in such claims) held by ESL Partners, L.P., a Delaware limited partnership ("Partners") and ESL Investors, L.L.C., a Delaware limited liability company ("Investors"). Pursuant to Kmart Corporation's Plan of Reorganization, an affiliate of the Reporting Persons has in the past received shares of Common Stock of Kmart Holding Corporation (the predecessor to Sears Holdings Corporation ("Holdings")) which acquisitions have been reported on Forms 3 and 4 previously filed by the Reporting Persons and certain of the Reporting Persons may receive in the future shares of Common Stock on account of these same trade vendor/lease rejection claims as all trade vendor/lease rejection claims held by all persons continue to be reconciled.
(2) These securities are owned by Partners.
(3) These securities are owned by Investors.
(4) These securities may be deemed beneficially owned by RBS Partners, L.P., a Delaware limited partnership ("RBS"). See Notes 12 and 13.
(5) These securities may be deemed beneficially owned by ESL Investments, Inc., a Delaware corporation ("ESL"). See Notes 12 and 13.
(6) These securities may be deemed beneficially owned by Edward S. Lampert. See Notes 12 and 13.
(7) These securities are owned by CRK Partners, LLC, a Delaware limited liability company ("CRK LLC").
(8) These securities are owned by ESL Investment Management, LLC, a Delaware limited liability company ("Investment Management").
(9) These securities are owned by ESL Institutional Partners, L.P., a Delaware limited partnership ("Institutional").
(10) These securities may be deemed beneficially owned by RBS Investment Management, L.L.C., a Delaware limited liability company ("RBSIM"). See Notes 12 and 13.
(11) These securities are owned by CRK Partners II, L.P., a Delaware limited partnership ("CRK II").
(12) This Form 4 is filed on behalf of a group consisting of ESL, Edward S. Lampert, CRK LLC, CRK II, Investors, Partners, Institutional, Investment Management, RBS and RBSIM. Mr. Lampert is the sole shareholder, chief executive officer and a director of ESL and the managing member of Investment Management and the Chairman and a director of Holdings. ESL is the general partner of RBS, the sole member of CRK LLC and the managing member of RBSIM. RBS is the managing member of Investors and the general partner of Partners. RBSIM is the general partner of Institutional. Pursuant to Rule 16a-1(a)(2), each of ESL, Mr. Lampert, RBS and RBSIM may be deemed to be the beneficial owner of the securities reported herein.
(13) The total amount of securities reported as benefically owned by CRK LLC, Investors, Partners, and Institutional is greater than ESL's or Mr. Lampert's indirect pecuniary interest in the securities owned by such persons. The total amount of securities reported as beneficially owned by Investment Management is greater than Mr. Lampert's indirect pecuniary interest in the securities owned by such persons. The total amount of securities reported as beneficially owned by Investors and Partners is greater than RBS's indirect pecuniary interest in the securities owned by such persons. The total amount of securities reported as beneficially owned by Institutional is greater than RBSIM's indirect pecuniary interest in the securities owned by such person. CRK II expressly disclaims beneficial ownership of the securities reported herein.

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