OUTLINE: This is a multicenter study. Part I (courses 1 and 2): Patients are assigned to 1 of 2 treatment groups based on prior cisplatin-based chemotherapy regimen: Group 1 (prior cisplatin with paclitaxel): Patients receive cisplatin IV over 1 hour on day 1 and fluorouracil IV continuously on days 1-4. Group 2 (prior cisplatin with fluorouracil): Patients receive cisplatin IV over 1 hour and paclitaxel IV over 3 hours on day 1. Both groups: Treatment repeats every 3 weeks for 2 courses. Patients who achieve partial or complete response after completion of course 2 are taken off study. Patients with stable disease or disease progression after completion of course 2 proceed to part II of the study. Part II (courses 3-6): Patients are stratified by response to initial cisplatin-based chemotherapy regimen (stable disease vs disease progression). Patients receive a test dose of cetuximab IV over 10 minutes on day 1. Patients who do not experience grade 4 anaphylactic reaction receive a loading dose of cetuximab IV over 2 hours beginning 30 minutes after completion of test dose. Patients receive cisplatin IV over 1 hour beginning 1 hour after completion of cetuximab infusion on day 1. Patients receive maintenance cetuximab IV over 1 hour on day 8. Maintenance cetuximab repeats weekly. Combination treatment repeats every 3 weeks for a maximum of 4 courses. Patients with stable or responding disease after completion of course 6 may continue to receive cetuximab alone in the absence of disease progression and at the discretion of the protocol investigator and sponsor. Quality of life is assessed before course 1, at the completion of courses 2, 4, and 6, and then at 4 weeks after completion of study. Patients are followed at 4 weeks.