OUTLINE: Patients are stratified by stage (III vs IV) and volume of residual disease (less than 3 cm vs at least 3 cm). Approximately 10-15 days after surgery, patients receive filgrastim (G-CSF) subcutaneously daily until all peripheral blood stem cell (PBSC) collections have been completed. Patients then receive carmustine IV over 2 hours on day -2 and melphalan IV over 20 minutes on day -1. Peripheral blood stem cells are infused 24 hours after melphalan on day 0. Patients receive G-CSF subcutaneously beginning on day 6 and continuing until granulocytes have recovered. Three months after the PBSC infusion, patients receive consolidation therapy with paclitaxel IV over 6 hours on day 2 and cisplatin IV over 24 hours on day 3. Consolidation treatment is repeated every 3 months for a total of 4 courses. Quality of life questionnaires are completed prior to PBSC transplant, before discharge after transplant, before each consolidation treatment, and 3 months after the last consolidation course. Patients are followed at least every 3 months for the first 2 years, and then every 6 months thereafter.