OUTLINE: This is a dose escalation study. Patients receive paclitaxel IV over 1 hour followed 2 hours later by gemcitabine IV over 30 minutes on days 1, 15, and 29. Treatment repeats every 6 weeks for a maximum of 8 courses. Cohorts of 3-5 patients receive escalating doses of paclitaxel and gemcitabine until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 5 patients experience dose limiting toxicity. Once the MTD is reached, an additional 14 patients (chemotherapy naive) with advanced NSCLC are treated at the recommended phase II dose. Patients are followed every 8 weeks for 6 months.