Inclusion Criteria: * Patients with: non-Hodgkin's lymphoma, Hodgkin's disease, acute myelogenous leukemia, acute lymphoblastic leukemia, chronic myelogenous leukemia, chronic lymphocytic leukemia, or multiple myeloma * Eligible for fractionated total body irradiation (fTBI) plus high-dose chemotherapy followed by autologous PBPC support. * 18 years of age or older * Karnofsky performance status greater than or equal to 70% * Minimum of 1.5 Mio CD34+ cells/kg cryopreserved and to be transplanted * Informed consent for participation in the study Exclusion Criteria: * History of, or concurrent cancer other than NHL, Hodgkin's disease, AML, ALL, CML, CLL, multiple myeloma * Prior bone marrow or peripheral blood stem cell transplantation * Purged stem cell product * Currently active infection or oral mucositis * Congestive heart failure * Serum creatinine > 1.5x ULN * Direct bilirubin > 1.5x ULN * Transaminases > 3x ULN * Corrected DLCO < 50% of predicted * Subject is currently enrolled in, or has not yet completed at least 30 days since ending other investigational device or drug trial(s) or is receiving other investigational agent(s). * Subject is pregnant (eg, positive human chorionic gonadotropin [HCG] test) or is breastfeeding. * Subject refuses to use adequate contraceptive precautions. * Known hypersensitivity to any of the products to be administered during dosing, including E coli-derived products. * Inability to give a truly informed consent.