OUTLINE: This is an open label, 2 part, multicenter study. Part 1 is a randomized, dose escalation, 2 period, 2 sequence, crossover design. Part 2 is a nonrandomized, single dose evaluation design. Part 1: Patients are randomized to receive ZD 1839 beginning 1 week before either the first (arm I) or second (arm II) course of carboplatin and paclitaxel. Arm I: Patients receive oral ZD 1839 daily on days 1-14. On day 1 only, ZD 1839 is given twice at 12 hour intervals. Patients receive paclitaxel IV over 3 hours followed by carboplatin IV over 30 minutes on days 8 and 36. Subsequent courses consist of ZD 1839 for 14 days and paclitaxel and carboplatin every 28 days. Arm II: Patients receive paclitaxel and carboplatin as in arm I on days 1 and 29. Patients receive oral ZD 1839 daily on days 22-35. On day 22 only, ZD 1839 is given twice at 12 hour intervals. Subsequent courses are administered as in arm I. Part 2: Patients receive oral ZD 1839 daily on days 1-56. On day 1 only, ZD 1839 is given twice at 12 hour intervals. Patients receive paclitaxel and carboplatin as in part 1 on days 8 and 36. Subsequent courses consist of ZD 1839 continuously and paclitaxel and carboplatin every 28 days. Treatment continues in both parts for a maximum of 6 months in the absence of unacceptable toxicity or disease progression. In both parts 1 and 2, cohorts of 6-12 patients receive escalating doses of ZD 1839 until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 4 of 6 or 4 of 12 patients experience dose limiting toxicities.