Exhibit 32.1

 (a) Certification of Quarterly Report by Chief Executive Officer.

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of GraphOn Corporation (the “Company”) on Form 10-Q for the period ended March 31, 2010 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Robert Dilworth, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Robert Dilworth

Robert Dilworth

Chief Executive Officer

May 13, 2010

(b) Certification of Quarterly Report by Chief Financial Officer.

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of GraphOn Corporation (the “Company”) on Form 10-Q for the period ended March 31, 2010 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, William Swain, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ William Swain

William Swain

Chief Financial Officer

May 13, 2010