I. To establish the safety profile of daily oral administration of ZD1839 ("Iressa", AstraZeneca, Inc.) that can be given with concurrent irradiation alone or combined concurrently with weekly cisplatin in previously untreated patients with locally advanced HNSCC, AJCC clinical stage III-IVB, deemed not suitable for surgery. Hence, the maximum-tolerated dose of ZD1839 will be determined.