SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT
                         PURSUANT TO SECTION 13 OR 15(D)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                         Date of Report: March 31, 2004

                         BioCryst Pharmaceuticals, Inc.

               (Exact Name of Registrant as Specified in Charter)

           Delaware                       000-23186               62-1413174
 (State or other jurisdiction            (Commission             (IRS Employer
      of incorporation)                 File Number)           Identification #)

               2190 Parkway Lake Drive, Birmingham, Alabama 35244
                     (Address of Principal Executive Office)

                                 (205) 444-4600
              (Registrant's telephone number, including area code)



Item 5. Other Events and Regulation FD Disclosure.

      On March 31, 2004, Registrant issued a press release announcing the
initiation of a Phase II clinical trial of BCX-1777 in T-cell leukemia. The
press release is being filed as Exhibit 99.1 to this Current Report on Form 8-K.

      Neither the filing of any press release as an exhibit to this Current
Report on Form 8-K nor the inclusion in such press release of a reference to
Registrant's Internet address shall, under any circumstances, be deemed to
incorporate the information available at such Internet address into this Current
Report on Form 8-K. The information available at Registrant's Internet address
is not part of this Current Report on Form 8-K or any other report filed by
Registrant with the Securities and Exchange Commission.

Item 7. Exhibits.

      Exhibit No.                        Description

            99.1  Press release dated March 31, 2004 entitled "BioCryst
                  Pharmaceuticals Initiates Phase II Clinical Trial of BCX-1777
                  in T-Cell Leukemia".



                                   SIGNATURES

      Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

Dated: March 31, 2004                     BioCryst Pharmaceuticals, Inc.


                                          By: /s/ Michael A. Darwin
                                              -------------------------
                                              Michael A. Darwin
                                              Chief Financial Officer and Chief
                                              Accounting Officer



                                  EXHIBIT INDEX

            Item                        Description

            99.1  Press release dated March 31, 2004 entitled "BioCryst
                  Pharmaceuticals Initiates Phase II Clinical Trial of BCX-1777
                  in T-Cell Leukemia".