OUTLINE: This is a randomized study. Patients are stratified according to histology (large B-cell vs other) and risk group (low/low-intermediate vs high-intermediate/high). Patients are randomized to one of two treatment arms. Arm I: Patients receive etoposide IV over 1 hour on days 1-3, carboplatin IV over 1 hour on day 2, ifosfamide IV continuously for 24 hours on day 2, and filgrastim (G-CSF) subcutaneously (SC) on days 5-12. Treatment continues every 3 weeks for 3 courses in the absence of disease progression or unacceptable toxicity. Arm II: Patients receive rituximab IV on day 1, etoposide IV over 1 hour on days 2-4, carboplatin IV over 1 hour on day 3, ifosfamide IV continuously for 24 hours on day 3, and G-CSF SC on days 6-13. Patients also receive rituximab IV on day 8 of course 1. Treatment continues every 3 weeks for 3 courses in the absence of disease progression or unacceptable toxicity. Patients are followed every 3 months for 1 year, every 6 months for 2 years, and then annually for 5 years.