Recent advances in allogeneic hematopoietic cell transplantation (allo-SCT) have led to reduce intensity preparative regimens that are non-myeloablative and reduce the toxicities associated with the transplant. Consequently non-relapse mortality has been reduced, including in elderly patients with comorbidities. However, despite this benefit in terms of toxicity, excessive reduction of the intensity preparative regimens may favor relapse of the initial illness. Thus, acute and chronic graft-versus-host disease and opportunistic fungal and viral infections are always serious complications. The aim of our study is to check if a new modality of reduced intensity preparative regimen combining total lymphoid irradiation (TLI) and thymoglobulin (ATG), would limit the toxicity of treatment and reduce the incidence of acute GVHD after allogeneic transplantation while preserving the antitumor benefit.