Exhibit 10.2 AMENDMENT NO. 2 TO THE NACCO INDUSTRIES, INC. SUPPLEMENTAL ANNUAL INCENTIVE COMPENSATION PLAN (AS AMENDED AND RESTATED EFFECTIVE AS OF JANUARY 1, 2001) The Compensation Committee of the Board of Directors of the Company hereby adopts this Amendment No. 2 to the NACCO Industries, Inc. Supplemental Annual Incentive Compensation Plan (As Amended and Restated Effective as of January 1, 2001) (the "Plan") effective as of January 1, 2005. Words and phrases used herein with initial capital letters that are defined in the Plan are used herein as so defined. Section 1 Section 2(b) of the Plan is hereby amended by deleting the phrase "Nominating, Organization and Compensation Committee" and replacing it with the phrase "Compensation Committee" therein. Section 2 The first sentence of Section 5(b) of the Plan is hereby amended in its entirety to read as follows: "No later than the March 15th of the following calendar year, the Committee shall approve (i) a preliminary calculation of the amount of each Award based upon the application of the formula and actual performance to the Target Awards previously determined in accordance with Section 5(a); and (ii) a final calculation of the amount of each Award to be paid to each Participant for the prior year." Section 3 Section 5 of the Plan is hereby amended by adding the following new Subsection (e) to the end thereof, to read as follows: "(e) Notwithstanding any provision of the Plan to the contrary, Awards payable hereunder shall be paid within two and one-half months after the end of the calendar year to which the Award relates." NACCO STIP/LTIP - Amend 2 Supplemental