Rule 424(b)(3)
                                                            File No.  333-06955
                             NALCO CHEMICAL COMPANY

                         COMMON STOCK ACQUIRED UNDER THE
                             NALCO CHEMICAL COMPANY
                 NON-EMPLOYEE DIRECTORS STOCK COMPENSATION PLAN
                          APPENDIX DATED JUNE 23, 1998
                                       TO
                         PROSPECTUS DATED JUNE 27, 1996

This Appendix updates certain  information in the Prospectus dated June 27, 1996
(the  "Prospectus")  relating to shares of Common  stock which may be offered by
the stockholders  listed herein under the caption  "Selling  Stockholders" or by
their  transferees  (or by their donees or  pledgees).  The Company will furnish
without charge to participants additional copies of the Prospectus upon request.


                              SELLING STOCKHOLDERS

The following  table sets forth the name and position within the Company for the
last three  years of each  Selling  Stockholder,  the number of shares of Common
Stock  of the  Company  beneficially  owned  by  him/her  on the  date  of  this
Prospectus, and the number of shares offered by the Prospectus.

                             Shares Owned                     Shares Offered by
Name of Director            Beneficially (1)                 This Prospectus (2)
- ----------------           ----------------                 -------------------
J. L. Ballesteros               16,600                                  600
H. G. Bernthal                  37,014(4)                               600(5)
H. Corless                      38,614(3)(4)                            600(5)
H. M. Dean                      33,864(3)(4)                            600(5)
J. P. Frazee, Jr.               39,248(4)                               600(5)
A. L. Kelly                     33,483(3)(4)                            600(5)
B. S. Kelly                      4,600                                  200
F. A. Krehbiel                  40,614(4)                               600(5)
S. A. Penrose                    6,206(4)                               200(5)
W. A. Pogue                     32,950(3)(4)                            600(5)
J. J. Shea                      25,614(4)                               600(5)

(1) Includes shares which may be acquired by exercise of stock options.
(2)  This does not  constitute a commitment  to sell all of the stated number of
     shares.  The amount of shares offered shall be determined from time to time
     by each Selling Stockholder in his/her sole discretion.
(3)  Includes  beneficial/ownership  of shares held  indirectly  by wife or by a
trust.

(4) Includes stock  compensation  deferred as Share Units from the  Non-Employee
Directors Stock Compensation Plan.
(5) Deferred as Share Units

Additional Selling Stockholders will be identified by a subsequent appendix.

One or more of the Selling  Stockholders may from time to time make gifts of any
or all of his/her  shares or pledge any or all of his/her  shares as  collateral
for loans.  In the event of such gift or of a default  under any such loan,  the
donee may elect to sell  donated  shares or the lender may elect to sell  shares
held as collateral by means of the Prospectus as supplemented.