OUTLINE: This is a randomized, multicenter study. Patients are stratified by center, histology (diffuse small cleaved cell, diffuse mixed, and diffuse large cell vs immunoblastic large cell, mantle cell, and marginal zone), and risk group (low vs intermediate vs high). Patients enter one of two treatment arms: Arm I: Patients receive rituximab IV on day 1, followed by cyclophosphamide IV, doxorubicin IV, vincristine IV, and oral prednisone for 5 consecutive days beginning on day 3. Arm II: Patients receive cyclophosphamide IV, doxorubicin IV, vincristine IV, and oral prednisone daily for 5 consecutive days beginning on day 1. Treatment repeats every 21 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients will be followed for 3 years.