This is a pilot study designed to evaluate the toxicity of a five day infusion of Paclitaxel concurrent with radiation therapy for advanced head and neck cancers. Patients with previously untreated Stage III and IV squamous cell cancer (SCC) of the oral cavity, oropharynx, hypopharynx, nasopharynx, larynx and maxillary sinus, as well as Stage II SCC of the base of the tongue, nasopharynx, and maxillary sinus will be eligible. Radiation therapy will be delivered at 180 cGy per day to a total dose 6660-7200 cGy. Individual neck nodes can be boosted with electrons up to 7600 cGy. Patients will also receive Paclitaxel as a continuous IV infusion of 120 mg/m(2) over 120 hours through a central venous catheter. Tolerance of this regimen will be judged by using the RTOG and CTEP standard toxicity criteria and by following the median elapsed treatment time. Serial tumor biopsies will be obtained to measure the following parameters: tumor potential doubling time (Tpot), paclitaxel levels in tumor, and biological effects upon the cell cycle.