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: May 11, 2004



                               GRAPHON CORPORATION
             (Exact name of Registrant as specified in its charter)



        Delaware                   0-21683                    13-3899021
       (State of            (Commission File No.)            IRS Employer
     incorporation)                                    Identification Number)



                   105 Cochrane Circle, Morgan Hill, CA 95037
                    (Address of principal executive offices)


                  Registrant's telephone number: (800) 472-7466






Item 12.  Results of Operations and Financial Condition.



On May 11, 2004, GraphOn Corporation issued a press release announcing its
financial results for the quarter ended March 31, 2004. A copy of the press
release is being furnished as Exhibit 99.1 to this report and incorporated
herein by reference.








                                   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 thereunto duly authorized.

Dated: May 12, 2004                       GRAPHON CORPORATION
                                             (Registrant)

                                    By:   /s/ William Swain
                                          -----------------------
                                          William Swain
                                          Chief Financial Officer