OBJECTIVES: I. Determine the response rate and toxicity profile of concurrent and consolidative chimeric anti-CD20 monoclonal antibody IDEC-C2B8 (rituximab) therapy compared to consolidative rituximab therapy in patients with chronic lymphocytic leukemia treated with fludarabine. II. Assess the complete response (CR) rate in patients receiving concurrent therapy with rituximab and fludarabine. III. Assess the frequency of conversion of a partial response (PR) to a CR or stable disease to either PR or CR in patients receiving consolidative therapy with rituximab. IV. Follow the effects of rituximab and fludarabine on the immunologic markers CD4, CD8, IgG, IgA, and IgM. V. Assess the progression-free and overall survival of these patients.