OUTLINE: This is an open label, dose escalation study. Patients receive paclitaxel IV over 3 hours on day 1. On day 2, patients receive cisplatin IV over 20 minutes followed by a 24 hour infusion of flavopiridol. Courses are repeated every 21 days in the absence of disease progression or unacceptable toxicity. Sequential dose escalation of flavopiridol is followed by sequential dose escalation of cisplatin. Dose escalation in cohorts of 3-6 patients each continues until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 6 patients experience dose limiting toxicity. Patients are followed every 6 weeks.