<PAGE>
                                                                  Exhibit 10(zz)

                                SECOND AMENDMENT
                                       TO
                   CLEVELAND-CLIFFS INC NONEMPLOYEE DIRECTORS'
                   -------------------------------------------
                                COMPENSATION PLAN
                                -----------------

                                    RECITALS
                                    --------

         WHEREAS, Cleveland-Cliffs Inc ("Company"), with approval of the
Company's shareholders on May 14, 1996, established the Cleveland-Cliffs Inc
Nonemployee Directors' Compensation Plan ("Plan"), effective July 1, 1996;

         WHEREAS, with the approval of the Board of Directors of the Company,
the Plan was amended by the First Amendment to the Plan on November 12, 1996;

         WHEREAS, the Company desires to amend the Plan further to provide for
an election to defer receipt of dividends declared and paid on Restricted Shares
("Second Amendment"); and

         WHEREAS, the Board of Directors of the Company has approved the Second
Amendment in accordance with the provisions of Section 8.2 of the Plan and such
Second Amendment does not require approval by the shareholders of the Company.

         NOW, THEREFORE, the Plan is hereby amended as follows:

         1. The Plan is amended, effective May 13, 1997, by adding the following
paragraph (e) to Section 3.1 of the Plan:

                  "(e) A Director who was awarded Restricted Shares on or before
         May 13, 1997, may elect within 30 days after such date that all cash
         dividends declared after May 13, 1997 with respect to such Restricted
         Shares during the period of such restrictions shall be deferred and
         reinvested in additional Common Shares which shall be subject to the
         same restrictions as the underlying award. All such deferred dividends
         (based on the number

                                        1


<PAGE>


         of Restricted Shares, including the then determined reinvested
         additional Common Shares) shall be reinvested and shall be delivered as
         additional unrestricted Common Shares on the applicable Vesting Date,
         subject to proration as provided in Section 3.1(c) hereof. A Director
         who receives an award of Restricted Shares after May 13, 1997, may
         likewise elect such deferral not later than 30 days after becoming a
         Director."

         2. Except as amended by the First Amendment and this Second Amendment,
the Plan shall remain in full force and effect.

         Executed in Cleveland, Ohio, as of May 13, 1997.

                                        CLEVELAND-CLIFFS INC

                                        By /s/ M.T. Moore
                                          --------------------------------------
                                            Chairman and Chief Executive Officer

                                        And /s/ J.E. Lenhard
                                           -------------------------------------
                                            Secretary

                                        2