Pricing Supplement No. 2 dated June 8, 1998                Rule 424(B)(3)
(To Prospectus dated April 1, 1996                         File No. 33-58887
and Prospectus Supplement dated April 1, 1996)

                           Colgate-Palmolive Company

                        Medium-term Notes - Fixed Rate

                                   Series C

Principal Amount: $25,000,000              Trade Date:   June 8, 1998
Issue Price:      100%                     Original Issue Date:   June 26, 1998
Interest Rate:    6.75% per annum          Net Proceeds to Issuer:  See 
                                                "Supplemental Plan of 
                                                 Distribution" below.
                                           Agent's Discount or Commission:  See
                                                 "Supplemental Plan of 
                                                  Distribution" below.

Stated Maturity Date:      June 26, 2018

Interest Payment Dates:    Semi-Annually (See "Other Provisions - Interest" 
                           below).

Day Count Convention:

         [ X ]    30/360 for the period from June 26, 1998 to June 26, 2018
         [   ]    Actual / 360 for the period from          to 
                                                   --------     --------

         [   ]    Actual / Actual for the period from         to
                                                      -------     -------

Redemption:

         [   ]    The Notes cannot be redeemed by the Company prior to 
                      the Stated Maturity Date, except as set forth 
                      in the Prospectus.
         [ X ]    The Notes may be redeemed by the Company prior to the 
                      Stated Maturity Date. Initial Redemption Date: 
                      June 26, 1999 (See "Other Provisions--Optional 
                      Redemption" below).

                  Initial Redemption Percentage:   100%

                  Annual Redemption Percentage Reduction:  N/A% until 
                                                           ---
                  Redemption Percentage is 100% of the Principal amount.

Optional Repayment:

         [ X ]        The Notes cannot be repaid at the option of the holder 
                        thereof prior to the Stated Maturity Date,
                        except as set forth in the Prospectus.
         [   ]        The Notes can be repaid at the option of the holder 
                        thereof prior to the Stated Maturity Date at
                        Optional Repayment Date(s):

                        Repayment Price:        %
                                         -------

Currency:

         Specified Currency:        US Dollars
              (If other than US Dollars, see attached.)
         Minimum Denomination: $1,000

        (Applicable only if Specified Currency is other than US Dollars.)





Original Issue Discount: [   ]      [ X ]   No
         Total amount of OID:
         Yield to Maturity:
         Initial Accrual Period:

Form:        [ X ]    Book-entry      [   ]        Certificated

Agent action in the capacity indicated below:
             [   ]    Agent            Principal  [ X ]

If as Principal:

               [X ]    The Notes are being offered at varying
                         prices related to prevailing market prices at
                         the time of resale.
               [  ]    The Notes are being offered at a fixed
                         initial public offering price of 100% of
                         principal amount.

If as Agent:
    The Notes are being offered at a fixed initial public offering price 
               of 100% of principal amount.

[ X ]         Other provisions:                 (see attached)

                           Bear, Stearns & Co. Inc.





Other Provisions:
- - ----------------

Interest:

         Interest on the Notes will accrue from June 26, 1998 and will be
         payable in U.S. dollars on the 26th day of June and December of each
         year, commencing December 26, 1998 up to and including the Stated
         Maturity Date (with respect to the final interest accrual period,
         interest on the Notes will accrue from and including the preceding
         Interest Payment Date on June 26, 2018 to but excluding the Stated
         Maturity Date) or date of earlier redemption (each, an "Interest
         Payment Date"). Interest will accrue from and including each Interest
         Payment Date to but excluding the next succeeding Interest Payment
         Date. In the event an Interest Payment Date falls on a day other than
         a Business Day, interest will be paid on the next succeeding Business
         Day and no interest on such payment shall accrue for the period from
         and after such Interest Payment Date to such next succeeding Business
         Day.

Optional Redemption:

         The Company may at its option elect to redeem the Notes in whole on
         June 26, 1999 or on any Interest Payment Date thereafter (each such
         date, an "Optional Redemption Date") at 100% of their principal
         amount plus accrued interest to but excluding the date of redemption
         (the "Redemption Date"). In the event the Company elects to redeem
         the Notes, notice will be given to registered holders not more than
         60 nor less than 30 days prior to the Redemption Date.

Certain Investment Considerations:
- - ---------------------------------

         Prospective purchasers should be aware that the Company has the
         option to redeem the Notes on any Optional Redemption Date and will
         be likely to elect to redeem the Notes in the event prevailing market
         interest rates are lower than the then-current interest rate on the
         Notes.

Use of Proceeds:
- - ---------------

The net proceeds from the sale of the Notes will be used by the Company to
retire commercial paper which was issued by the Company for general corporate
purposes and working capital. As of June 12, 1998, the Company's outstanding
commercial paper had a weighted average interest rate of 5.5% with maturities
ranging from 1 to 155 days.

Supplemental Plan of Distribution:
- - ---------------------------------

         Under the terms of and subject to the conditions of an agreement,
         dated as of June 8, 1998, between Bear, Stearns & Co. Inc. and the
         Company, Bear, Stearns & Co. Inc., acting as principal, has agreed to
         purchase, and the Company has agreed to sell, the Notes at 100% of
         their principal amount. Such purchase price includes an amount
         related to a swap entered into by the Company and an affiliate of
         Bear, Stearns & Co. Inc. in connection with the issuance of the Notes.