The major aims of the trial are: (Phase 1b) to investigate the safety and tolerability of sequential dose cohorts and to determine a recommended Phase 2 dose for Hu5F9-G4 in combination with rituximab, and (Phase 2) to evaluate the efficacy of Hu5F9-G4 in combination with rituximab in patients with indolent lymphoma or diffuse large B-cell lymphoma as measured by the overall response rate.