Exhibit 13  CERTIFICATIONS UNDER SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002
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Pursuant  to  Section  906  of  the  Sarbanes-Oxley  Act of  2002,  each  of the
undersigned  certifies  that  this  periodic  report  fully  complies  with  the
requirements  of Section 13(a) or 15(d) of the  Securities  Exchange Act of 1934
and that information contained in this periodic report fairly represents, in all
material respects,  the financial  condition and results of operations of Nordic
American Tanker Shipping Limited.


/s/ Herbjorn Hansson

Herbjorn Hansson
Chief Executive Officer


/s/ Rolf Amundsen

Rolf Amundsen
Chief Financial Officer

Date: June 30, 2004