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                                 UNITED STATES           
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549      
                                                         

                                  SCHEDULE 13G
                           
                   UNDER THE SECURITIES EXCHANGE ACT OF 1934

                       (AMENDMENT NO. _________________)*

                               Cree Research Inc.
- --------------------------------------------------------------------------------
                                (NAME OF ISSUER)

                                     Common
- --------------------------------------------------------------------------------
                         (TITLE OF CLASS OF SECURITIES)

                                   225447101
                        --------------------------------
                                 (CUSIP NUMBER)


Check the following box if a fee is being paid with this statement [ ]. (A fee
is not required only if the filing person: (1) has a previous statement on file
reporting beneficial ownership of more than five percent of the class of
securities described in Item 1; and (2) has filed no amendment subsequent
thereto reporting beneficial ownership of five percent or less of such class.)
(See Rule 13d-7).

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).



                               Page 1 of 4 pages
   2

- ----------------------                               ---------------------------
 CUSIP NO.  225447101                13G              PAGE _____ of _____ PAGES
- ----------------------                               ---------------------------


- --------------------------------------------------------------------------------
1  NAME OF REPORTING PERSON
   S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON


                Driehaus Capital Management, Inc.

- --------------------------------------------------------------------------------
2  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

                                                                (a)   [ ]

                                                                (b)   [ ]

- --------------------------------------------------------------------------------
3  SEC USE ONLY



- --------------------------------------------------------------------------------
4  CITIZENSHIP OR PLACE OF ORGANIZATION


                ILLINOIS, U.S.A.
- --------------------------------------------------------------------------------
                        5  SOLE VOTING POWER


                             339,294
   NUMBER OF
    SHARES            ----------------------------------------------------------
  BENEFICIALLY          6  SHARED VOTING POWER
    OWNED BY
      EACH                   0
   REPORTING
    PERSON            ----------------------------------------------------------
     WITH               7  SOLE DISPOSITIVE POWER


                             717,697

                      ----------------------------------------------------------
                        8  SHARED DISPOSITIVE POWER


                             0

- --------------------------------------------------------------------------------
9  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON


                717,697

- --------------------------------------------------------------------------------
10 CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*



- --------------------------------------------------------------------------------
11 PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9


                5.62%

- --------------------------------------------------------------------------------
12 TYPE OF REPORTING PERSON*


                IA

- --------------------------------------------------------------------------------
                      *SEE INSTRUCTION BEFORE FILLING OUT!

                               Page 2 of 4 pages
   3



Driehaus Capital Management, Inc.
SCHEDULE 13G


Item 1.               (a)  Name of Issuer:  Cree Research Inc.

                      (b)  Issuer's Principal Executive Offices:

                           2810 Meridian Pkwy, Ste. 144
                           Durham, North Carolina  27713

Item 2.               (a)  Person Filing - Driehaus Capital Management, Inc.

                      (b)  Address - 25 East Erie Street
                                       Chicago, IL 60611

                      (c)  Citizenship - U.S.A.

                      (d)  Title of Class of Securities - Common

                      (e)  CUSIP Number - 225447101

Item 3.               (e)  Investment Adviser Registered under section 203 of 
                           the Investment Advisers Act of 1940.


Item 4.               (a)  Amount Beneficially Owned - 717,697

                      (b)  Percent of Class -  5.62%

                      (c)  Number of shares as to which reporting person has:
                           (i)   Sole voting power            339,294 
                           (ii)  Shared voting power              0
                           (iii) Sole dispositive power       717,697
                           (iv)  Shared dispositive power         0


Item 5.               Not Applicable


Item 6.               The reporting person, Driehaus Capital Management,
                      Inc., manages accounts for numerous clients on a fully
                      discretionary basis. Securities held in these clients'
                      accounts are included in this report to reflect the fact
                      that the reporting person may have voting power or
                      dispositive power. To the best of the reporting person's
                      knowledge, none of the clients whose securities are
                      included in this report have an ownership interest in the
                      subject class of securities which exceeds five percent of
                      the class.




                                                                     Page 3 of 4

   4



Driehaus Capital Management, Inc.
SCHEDULE 13G


Item 7.               Not Applicable


Item 8.               Not Applicable


Item 9.               Not Applicable


Item 10.              Certification


         By signing below I certify that, to the best of my knowledge and
         belief, the securities referred to above were acquired and are held in
         the ordinary course of business and were not acquired and are not held
         for the purpose of or with the effect of changing or influencing the
         control of the issuer of the securities and were not acquired and are
         not held in connection with or as a participant in any transaction
         having that purpose or effect.


                                    SIGNATURE

         After reasonable inquiry and to the best of my knowledge and belief, I
         certify that the information set forth in this statement is true,
         complete and correct.


                                 February 8, 1999
                                 ----------------------------------------------
                                                   Date

                                 /s/ Mary H. Weiss
                                 ----------------------------------------------
                                                 Signature


                                 Mary H. Weiss, Vice President
                                 ----------------------------------------------
                                                 Name/Title



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