This is a Phase II study of paclitaxel (Taxol R) administered as a 96-hour (4 day) continuous infusion followed by a bolus of cisplatin for previously untreated patients with stage III/IV or relapsed non-small cell lung cancer (NSCLC). The goal of this phase II study is to determine the response rate of this infusional paclitaxel and bolus cisplatin regimen in patients with advanced NSCLC. In addition, the plasma levels of paclitaxel will be measured, and the in vitro paclitaxel chemosensitivity of the tumor cells from as many patients as possible will be determined. This will allow further study of the relationship between in vitro drug sensitivity, achievable plasma concentrations of paclitaxel, and patients' response to therapy.