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.