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                                               Filed Pursuant to Rule 424(b)(2)
                                           Registration Statement No. 333-00117



                SUPPLEMENT NO. 7 TO PROSPECTUS SUPPLEMENT DATED
             JANUARY 26, 1996 AND PROSPECTUS DATED JANUARY 19, 1996

                            COOPER INDUSTRIES, INC.

                         THIRD SERIES MEDIUM-TERM NOTES

                             ISSUE DATE MAY 8, 1998

                                  
                                                  INTEREST RATE
MATURITY DATE                                      PER ANNUM
- -------------                                     -------------
                                                           
May 8, 2008                                           6.375%



Issued At 100% of Aggregate Principal Amount.
Not Redeemable Prior To Maturity.
Issue Initially In Book Entry Form.

The aggregate principal amount of this offering is $100,000,000.00 and relates
only to Supplement No. 7.  To date, including this offering, an aggregate of
$300,000,000.00 Third Series Medium-Term Notes has been issued.