This is a phase I study of paclitaxel as a radiation sensitizer in the treatment of unresectable mesothelioma and non-small cell lung cancer. The purpose is to determine the maximum tolerated dose of paclitaxel when delivered as a 20-hour continuous infusion every 3 weeks concurrently with thoracic irradiation to include the primary tumor site and appropriate draining lymph nodes for non-small cell lung cancer patients. Hemithorax irradiation will be employed for patients with mesothelioma. Another goal of this protocol is to understand the biology of lung cancer and mesothelioma as well as to assess the effectiveness of paclitaxel against these tumors. To achieve this goal, we will examine, among other studies, the labeling index of tumor specimens with the use of the in vivo iododeoxyuridine (IUudR) labeling technique. Studies of in vivo IUdR labeling at other centers include breast, lung, prostate, gastric, and colon carcinomas. There are very limited data from IUdR labeling of mesothelioma. We have, thus far, accrued 12 patients on this protocol. The current dose of paclitaxel is 120 mg/m2. Patients are assessed clinically for acute toxicity which is graded weekly per RTOG toxicity grading system. Patients have tolerated the treatment well and no significant increase in acute toxicity has been noted. All patients who have completed treatment so far have had improvement of symptoms (usually pain) and varying degrees of radiologic response.