Allogeneic stem cell transplantation is the treatment of choice for a growing number of malignant and non-malignant indications. Until recently, myeloablative in conjunction with immunosuppressive conditioning was considered mandatory for the elimination of malignant hematopoietic cells and to prevent graft rejection. The aim of allogeneic non-myeloablative stem cell transplantation (NST) is to induce host-to-graft tolerance with fast and durable engraftment of donor stem cells, by means of conditioning, which is well-tolerated by patients. The rationale behind the NST strategy is to induce optimal graft-versus-leukemia (GVL) effects for the elimination of all malignant cells by alloreactive immunocompetent cells from a matched donor as an alternative to standard high-dose myeloablative chemo radiotherapy. The NST protocol is therefore mainly based on immunosuppression and thus contains fludarabine, low dose busulfan and anti-T-lymphocyte globulin (ATG). Thymoglobuline is a polyclonal rabbit antiserum specific for human T cells used in organ transplantation for induction of tolerance and rejection prevention and treatment. It was also used in stem-cell transplantation (SCT) for the same purposes (e.g. for generation of tolerance and rejection preclusion) as well as a treatment for graft-versus-host disease (GVHD). Data from myeloablative protocols suggest that ATG before SCT significantly reduces the risk for grade III-IV acute GVHD. This does not translate to a reduction in transplant-related mortality (TRM) because of the increased risk for infections and thus survival is unchanged. Extensive chronic GVHD was also significantly shown to be reduced in patients receiving ATG in the myeloablative setting. However, the role of ATG in the NST protocol was never evaluated in a prospective randomized trial. In view of the preliminary data suggesting of an additive effect of ATG in these circumstances we, the investigators at Hadassah Medical Organization, evaluate the effect of ATG in NST by a prospective randomized trial.