Currently, standard treatment for locally advanced NPC in the U.S. consists of concomitant cisplatin with radiation followed by 3 courses of cisplatin and 5-fluorouracil. This, or comparable standard therapies will be considered part of standard therapy and patients will be considered for accrual three or more months after its completion. Patients must demonstrate evidence of local control with no histological or radiological evidence of recurrent disease three months after the end of standard therapy and be, otherwise, clinically disease free at the time of protocol entry as documented by radiological studies within 6 weeks of patient entry. Physical and histological evidence of disease recurrence at the time of patients' screening and during follow up will be performed under the supervision of Dr. Carter Van Waes during an out patient evaluation. Similar enrollment criteria will be used with patients who do not bear HLA-A*1101 or HLA-A*2402. However, these patients will be followed by observation only.