High-dose chemotherapy followed by autologous (the patient's own) peripheral blood (circulating blood) stem cell (cells that divide to form white cells, red cells and cells that help clot) transplantation is a conventional treatment for patients with lymphoma (cancer of lymph glands) and Hodgkin's disease (cancer of lymph glands) after first relapse (recurrence of disease). For patients who did not have a complete response after traditional chemotherapy, the chance is high that the tumor will return even after high-dose chemotherapy. To improve the response and decrease the chance of relapse, doctors have used rituximab, an antibody that kills lymphoma cells, both before and after transplantation. These doctors have reported that more patients had control of the tumor for an extended period of time using rituximab with high-dose chemotherapy with autologous stem cell transplantation. How widely this is applicable is not known.