<PAGE>
                                                                   EXHIBIT 10.35

                                   AGREEMENT

          This Agreement (this "Agreement") is made and entered into as of
January 19, 2005, by and among Kmart Management Corporation, a Michigan
corporation (the "Company"), Kmart Holding Corporation, a Delaware corporation
and the Company's parent corporation ("Holding Corp."), and Harold Lueken (the
"Executive").

          WHEREAS, the Executive and the Company are party to an Employment
Agreement made and entered into on May 6, 2003 (the "Employment Agreement"), and
the Executive has been serving as Senior Vice President, General Counsel of the
Company and Holding Corp.;

          WHEREAS, the Company and the Executive have mutually agreed that the
Executive will cease to be so employed and to so serve on January 31, 2005 (the
"Effective Date"); and

          NOW, THEREFORE, the Company, Holding Corp. and the Executive hereby
agree as follows:

          1. Resignation.  The Executive hereby resigns, as of the Effective
Date, from his employment with the Company and Holding Corp. and from all other
positions the Executive holds as an officer or member of the board of directors
of any of the subsidiaries or affiliates of Holding Corp. and the Company. The
Company acknowledges that Executive shall not be required to report for work to
the Company's headquarters offices in January 2005.

          2. Salary.  The Company shall continue to pay the Executive his base
salary, at its current rate, through the Effective Date.

          3. Severance Payments and Benefits.  (a) The Company shall, on the
Effective Date, execute a release attached hereto as Exhibit A (the "Release").
The Executive shall, on the Effective Date, execute the Release, and shall be
entitled to receive the payments and benefits provided for in this Section 3,
but only if he executes and does not revoke the Release, and if he complies with
his obligations under the provisions of the Employment Agreement that continue
in effect pursuant to Section 4 below. Notwithstanding anything to the contrary
in this Section 3, no payment shall be made pursuant to this Section 3 prior to
the first date that such payment would not subject the Executive to the 20%
additional tax imposed by Section 409A of the Internal Revenue Code of 1986, as
amended.

          (b) Subject to Section 3(a) above, the Company shall pay the Executive
his base salary for a period of one year commencing on the Effective Date, in
the manner, and subject to the reductions, set forth in Section 10(d)(ii)(B) of
the Employment Agreement.

          (c) Subject to Section 3(a) above, the Executive shall also be
eligible for his annual bonus for the fiscal year beginning January 29, 2004
(such bonus, the "2004 Annual Bonus"), computed and payable in accordance with
its terms as in effect as of the Effective Date, as set forth in and subject to
Exhibit B hereto, based on actual performance for the entire fiscal year. The
2004 Annual Bonus (if any) shall be paid at the same time as bonuses for 2004
are generally paid under the applicable bonus plan.

<PAGE>

          (d) Subject to Section 3(a) above, the Company shall pay the
Executive, in lieu of any outstanding Long Term Incentive Awards to the
Executive, $750,000 in a cash lump sum, on the date when the Release is first
irrevocable by its terms.

          (e) The Executive holds restricted shares of Holding Corp. that were
granted to him pursuant to a Restricted Stock Agreement between the Executive
and the Company, effective as of September 3, 2003 (the "Restricted Stock
Agreement") (such shares, the "Restricted Stock"). The Restricted Stock has
previously vested and become free of transfer restrictions with respect to 5,703
shares. Subject to Section 3(a) above, as of the Effective Date, the Restricted
Stock shall vest and become free of transfer restrictions with respect to an
additional 5,703 shares. The remainder of the Restricted Stock shall be
forfeited as of the Effective Date.

          (f) Subject to Section 3(a) above, from the Effective Date through the
first anniversary thereof, the Executive shall be provided with continued
welfare benefits or the equivalent thereof, subject to reduction and otherwise
on the terms and conditions set forth in Section 10(d)(ii)(F) of the Employment
Agreement. The period during which the Executive is eligible for health
continuation coverage under the requirements of Section 601 et seq. of the
Employee Retirement Income Security Act of 1974, as amended, and Section 4980B
of the Internal Revenue Code of 1986, as amended (known as "COBRA coverage")
shall begin on the day after the Effective Date.

          (g) Subject to Section 3(a) above, the Executive shall be provided
with other or additional benefits in accordance with applicable plans and
programs of the Company or its affiliates.

          4. Continued Applicability of Certain Employment Agreement Provisions.
Sections 10(f) and (i), 11, 12, 14(c) and (d), 15, 16 and the last sentence of
Section 10(d) of the Employment Agreement shall continue to apply in accordance
with their terms following the Effective Date, as if they were part of this
Agreement.

          5. Entire Agreement; Amendments.  This Agreement sets forth the entire
agreement of the Company and the Executive with respect to the subject matter
hereof, and supersedes the Employment Agreement in its entirety except as
specifically provided herein. This Agreement may not be amended except in a
writing signed by the Executive and an authorized representative or
representatives of Holding Corp. and the Company.

          6. Successors.  (a) This Agreement is personal to the Executive and
shall not be assignable by the Executive, except by will or the laws of descent
and distribution. This Agreement shall inure to the benefit of and be
enforceable by the Executive's legal representatives.

          (b) This Agreement shall inure to the benefit of and be binding upon
the Company, Holding Corp. and their respective successors.

          7. Notices.  (a) Any notice given to a party to this Agreement shall
be in writing and shall be deemed to have been given when delivered personally
or sent by certified or


                                      -2-

<PAGE>

registered mail, postage prepaid, return receipt requested, duly addressed to
the party concerned at the address indicated below or to such changed address as
such party may subsequently give such notice of:

          If to the Company or Holding Corp.:

             Kmart Management Corporation
             3100 West Big Beaver Road
             Troy, MI 48084-3163
             Attention: Chief Executive Officer

             With a copy to: Attention: General Counsel (at the above address)

          If to the Executive:

             11790 Valencia Gardens Ave.
             Palm Beach Gardens, FL 33410

             With a copy to: hlueken@yahoo.com

          (b) The Company may withhold from any amounts payable under this
Agreement such Federal, state or local taxes as shall be required to be withheld
pursuant to any applicable law or regulation.

          IN WITNESS WHEREOF, each of the parties hereto has duly executed this
Agreement as of the date first set forth above.

                                        KMART MANAGEMENT CORPORATION


                                        By:
                                            ------------------------------------
                                        Title:


                                        KMART HOLDING CORPORATION


                                        By:
                                            ------------------------------------
                                        Title:


                                        THE EXECUTIVE


                                        ----------------------------------------
                                        Harold Lueken


                                      -3-

<PAGE>

                                    EXHIBIT A

                       MUTUAL COVENANT NOT TO SUE AND FULL
                        AND COMPLETE RELEASE OF LIABILITY

          8. In consideration of the payments and benefits set forth in the
Agreement (the "Agreement") dated as of January 15, 2005, by and among Kmart
Management Corporation, a Michigan corporation (the "Company"), Kmart Holding
Corporation, a Delaware corporation and the Company's parent corporation
("Holding Corp."), and Harold Lueken (the "Executive"), the Executive hereby
releases and forever discharges the Company, Holding Corp. and any affiliates or
divisions and their current and former directors, officers, employees and agents
(hereinafter referred to collectively as the "Company Releasees") from any and
all charges, complaints, claims, liabilities, obligations, promises, agreements,
controversies, damages, remedies, actions, causes of action, suits, rights,
demands, costs, losses, debts and expenses (including attorneys' fees and costs)
of any nature whatsoever, which the Executive or his heirs, administrators,
representatives, executors, successors and assigns may have had or may not have,
known or unknown, whether in law or equity and whether arising under federal,
state or local law, which has or may have arisen out of any act or omission
occurring on or prior to the date of the execution (the "Execution Date") of
this Mutual Covenant Not To Sue and Full and Complete Release of Liability
("Mutual Release"), including, but not limited to, all claims arising under or
in connection with the Michigan Elliott-Larsen Civil Rights Act, as amended,
Michigan Whistle Blowers' Protection Act, as amended, the Michigan Persons With
Disabilities Civil Rights Act, as amended, Age Discrimination in Employment Act
of 1967, as amended, Americans With Disabilities Act of 1990, as amended, Title
VII of the Civil Rights Act of 1964, as amended, Civil Rights Act of 1991, as
amended, Employee Retirement Income Security Act of 1974 ("ERISA"), as amended,
Older Workers Benefit Protection Act of 1990, as amended, the Worker Adjustment
Retraining and Notification Act, the Fair Labor Standards Act, as amended, the
Family & Medical Leave Act of 1993, as amended, the common law of the State of
Michigan and the common law and statutes of the State of Delaware, for tort,
breach of express or implied employment contract, wrongful discharge,
intentional infliction of emotional distress, and defamation or injuries
incurred on the job or incurred as a result of loss of employment. The release
described in this Paragraph 1 shall not apply to (i) any actions to enforce
rights arising under, or any claim for payments or benefits which may be due the
Executive under, the Agreement, or (ii) any claim for benefits which may be due
the Executive under any "employee benefit plan" (as defined in Section 3(3) of
ERISA) of the Company and its related or affiliated companies or divisions in
which he was a participant, other than any severance pay plan or any plan that
would result in any duplication of benefits. The Executive represents that he
has not filed against the Company Releasees any complaints, charges, or lawsuits
arising out of his employment, or any other matter arising on or prior to the
date of this Mutual Release. The Executive covenants and agrees that he will not
seek recovery against the Company Releasees arising out of any of the matters
released in this Paragraph 1.

          9. In consideration of the Executive's release set forth above and the
covenants contained herein, Holding Corp., the Company and their respective
subsidiaries and divisions, whether direct or indirect (for purposes of this
Mutual Release, collectively, "Kmart"), hereby release and forever discharge the
Executive and his heirs, administrators, representatives, executors, successors
and assigns from any and all charges, complaints, claims, liabilities,


                                      -4-

<PAGE>

obligations, promises, agreements, controversies, damages, remedies, actions,
causes of action, suits, rights, demands, costs, losses, debts and expenses
(including attorneys' fees and costs) of any nature whatsoever, whether known or
unknown, which has or may have arisen out of any act or omission occurring on or
prior to the Execution Date, including, but not limited to, all claims arising
under or in connection with the Executive's services as an employee, director or
consultant, the common law of the State of Michigan and the common law and
statutes of the State of Delaware, for tort, breach of express or implied
employment contract and defamation; provided, however, that nothing contained
herein shall constitute a waiver or release by Kmart of claims or causes of
action (i) arising out of illegal conduct by the Executive, or (ii) arising out
of the Agreement. Kmart represents that it has not filed against the Executive
any complaints, charges, or lawsuits arising out of any matter arising on or
prior to the date of this Mutual Release. Kmart covenants and agrees that it
will not seek recovery against the Executive arising out of any of the matters
released in this paragraph.

          10. Nothing in this Mutual Release shall limit either party from
filing a lawsuit or other action for the sole purpose of enforcing this Mutual
Release.

          11. The Executive, Holding Corp. and the Company agree that the acts
done and evidenced hereby, and the releases granted hereunder, are done and
granted to compromise any doubtful and disputed claims and to avoid litigation,
and are not an admission of liability on the part of Kmart or the Executive and
that any such liability is expressly denied.

          12. The Executive acknowledges that he has no seniority, recall,
reinstatement, or rehire rights with Kmart in any capacity.

          13. The Executive agrees that he will honor the restrictive covenants
set forth in the provisions referred to in Section 4 of the Agreement.

          14. If any provision or paragraph of this Mutual Release is ever
determined not to be enforceable, the remaining provisions and paragraphs shall
remain in full force and effect.

          15. The Executive acknowledges that: (i) this entire Mutual Release
and the Agreement are written in a manner calculated to be understood by him;
(ii) he has been advised to consult with an attorney before executing this
Mutual Release and the Agreement; (iii) he was given a period of twenty-one days
within which to consider this Mutual Release; and (iv) to the extent he executes
this Mutual Release before the expiration of the twenty-one-day period, he does
so knowingly and voluntarily and only after consulting his attorney. The
Executive shall have the right to cancel and revoke this Mutual Release during a
period of seven days following the Execution Date, and this Mutual Release shall
not become effective, and no payments or benefits shall be made or provided
pursuant to Section 3 of the Agreement, prior to the day after the expiration of
such seven-day period. In order to revoke this Agreement, the Executive shall
deliver to the Company, prior to the expiration of such seven-day period, a
written notice of revocation. Upon such revocation, this Mutual Release shall be
null and void and of no further force or effect.

          16. The Executive, Holding Corp. and the Company acknowledge that this
Mutual Release will be governed by and construed and enforced in accordance with
the internal


                                      -5-

<PAGE>

laws of the State of Michigan. If a dispute arises concerning any provisions of
this Mutual Release, it shall be resolved by arbitration in accordance with
Section 16 of the Employment Agreement (as defined in the Agreement).

          17. THE EXECUTIVE ACKNOWLEDGES THAT HE HAS READ THIS MUTUAL RELEASE,
THAT HE HAS BEEN PROVIDED 21 DAYS TO CONSIDER THIS MUTUAL RELEASE, THAT HE HAS
BEEN ADVISED THAT HE HAS 7 DAYS TO REVOKE HIS SIGNATURE, THAT HE HAS BEEN
ADVISED THAT HE SHOULD CONSULT WITH AN ATTORNEY BEFORE HE EXECUTES THIS MUTUAL
RELEASE, AND THAT HE UNDERSTANDS ALL OF ITS TERMS AND EXECUTES IT VOLUNTARILY
AND WITH FULL KNOWLEDGE OF ITS SIGNIFICANCE AND THE CONSEQUENCES THEREOF.

                                        HAROLD LUEKEN


                                        ----------------------------------------
                                        Date:
                                              ----------------------------------


                                        KMART HOLDING CORPORATION


                                        By:
                                            ------------------------------------
                                            [TITLE]

                                        Date:
                                              ----------------------------------


                                        KMART MANAGEMENT CORPORATION


                                        By:
                                            ------------------------------------
                                            [TITLE]

                                        Date:
                                              ----------------------------------


                                      -6-

<PAGE>

                                    EXHIBIT B
                                2004 ANNUAL BONUS

          The amount of the 2004 Annual Bonus shall be determined based upon the
Company's adjusted EBITDA (as defined in the Company's business plan) for the
fiscal year beginning January 29, 2004 as compared to a target amount of $730
million, but in no event shall Executive's bonus payment exceed 100% of his
target bonus. By way of example, if the Company achieves or exceeds the target
EBITDA of $730 million, the Executive shall receive 100% of his target 2004
Annual Bonus, or $274,500 (base salary of $450,000 x 61% target bonus per
Employment Agreement = $274,500).


                                      -7-