THE USE OF A CHIMERIC ANTI-CD20 ANTIBODY, RITUXAN®, AS AN IN VIVO OR IN VITRO PURGING AGENT, OF PATIENTS RECEIVING BONE MARROW OR PERIPHERAL BLOOD STEM CELL TRANSPLANT DURING TREATMENT OF B-CELL-RELATED MALIGNANCIES, E.G., B-CELL LYMPHOMAS OR LEUKEMIAS, IS DISCLOSED. SUCH PURGING MAY ENHANCE ENGRAFTMENT AND/OR PREVENT DISEASE RELAPSE IN SUCH PATIENTS.