 This multi-center, open-label, randomized study will evaluate the participant preference with subcutaneous versus intravenous administration of MabTheraRituxan rituximab in participants with CD20 diffuse large B-cell lymphoma or CD20 follicular non-Hodgkins lymphoma. In Arm A, participants will receive MabTheraRituxan 375 mgm2 intravenously IV on Day 1 of Cycle 1 and MabTheraRituxan 1400 mg subcutaneously SC on Day 1 of Cycles 2-4, followed by MabTheraRituxan IV in Cycles 5-8. Participants in Arm B will receive MabTheraRituxan IV in Cycles 1-4 and SC in Cycles 5-8. All participants will receive 6-8 cycles of standard chemotherapy according to local country practice with 8 cycles of MabTheraRituxan. Anticipated time on study treatment is up to 24 weeks. 