WARBURG PINCUS US CORE EQUITY FUND INC
N-8A, 1998-08-05
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<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM N-8A

                          NOTIFICATION OF REGISTRATION
                      FILED PURSUANT TO SECTION 8(a) OF THE
                         INVESTMENT COMPANY ACT OF 1940



         The undersigned investment company hereby notifies the Securities and
Exchange Commission that it registers under and pursuant to the provisions of
Section 8(a) of the Investment Company Act of 1940 and in connection with such
notification of registration submits the following information:

                        --------------------------------

Name:    WARBURG, PINCUS U.S. CORE EQUITY FUND, INC.

Address of Principal Business Office (No. & Street, City,
   State, Zip Code):

                              466 Lexington Avenue
                          New York, New York 10017-3147

             Telephone Number (including area code): (212) 878-0600

                Name and address of agent for service of process:

                               Mr. Eugene P. Grace
                  Warburg, Pincus U.S. Core Equity Fund, Inc.
                              466 Lexington Avenue
                          New York, New York 10017-3147

                                   Copies to:

                             Rose F. DiMartino, Esq.
                            Willkie Farr & Gallagher
                               787 Seventh Avenue
                          New York, New York 10019-6099

Check Appropriate Box:

     Registrant is filing a Registration Statement pursuant to Section 8(b)
   of the Investment Company Act of 1940 concurrently with the filing of Form
   N-8A:  Yes /X/     No / /
<PAGE>   2
                                   SIGNATURES


         Pursuant to the requirements of the Investment Company Act of 1940, as
amended, the registrant has caused this notification of registration to be duly
signed on its behalf in the City of New York and State of New York on the 20th
day of July, 1998.



                                 WARBURG, PINCUS U.S. CORE EQUITY
                                 FUND, INC.



                                 By: /s/Eugene P. Grace
                                     -----------------------------------
                                     Eugene P. Grace
                                     Vice President and Secretary


ATTEST:

By:/s/Janna Manes
   -----------------------
    Janna Manes
    Assistant Secretary



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