OUTLINE: This is a multicenter study. Patients are stratified according to center and tumor site (hypopharynx vs base of tongue). Base of tongue stratum closed as of November 15, 1998. Regimen A: Patients receive cisplatin IV over 90 minutes on days 1 and 22 and fluorouracil IV over 120 minutes on days 1-5 and 22-26. Patients with measurable neck nodes discontinue therapy if disease has progressed by day 22. All patients who achieve complete or partial response at day 43 proceed to regimen B. All others proceed to resection followed by radiotherapy (off study). Regimen B (begins within 3-4 weeks of start of second induction course): Patients receive cisplatin IV over 90 minutes every 3 weeks for 3 courses. Concurrently, patients receive radiotherapy 5 days a week for 5.6 weeks. Patients are reassessed at 8-12 weeks after radiotherapy. Patients who are disease free are observed. Other patients undergo surgical resection of nodes and/or primary tumor. Patients are followed every 4-6 weeks for 1 year, every 2 months for 1 year, every 4 months for 2 years, every 6 months for 1 year, then annually thereafter.