The study design is as follows: Patients with poor prognosis NHL receive rituximab as part of the peripheral blood progenitor cell mobilization process and as part of the preparative regimen in combination with high-dose chemotherapy. Granulocyte colony-stimulating factor (G-CSF) mobilized peripheral blood progenitor cells (PBPC) are collected and stored. After recovery from high-dose cyclophosphamide, patients are admitted to the hospital for transplant. The preparative regimen consists of rituximab, followed by high-dose chemotherapy.