Inclusion Criteria:  Patients must have an indication for allogeneic hematopoietic stem cell transplantation with myeloablative conditioning for malignant disease Patients with 5-9/10 HLA-matched related donor available. The donor and recipient must be identical by the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB1, and HLA-DQB1. Peripheral blood stem cells or bone marrow as a graft source No second malignancies requiring treatment No severe concurrent illness  Exclusion Criteria:  Titer of anti-HLA antibodies ≥ 5000 at the time of inclusion Moderate or severe cardiac dysfunction, left ventricular ejection fraction <50% Moderate or severe decrease in pulmonary function, FEV1 <70% or DLCO<70% of predicted Respiratory distress >grade I Severe organ dysfunction: AST or ALT >5 upper normal limits, bilirubin >1.5 upper normal limits, creatinine >2 upper normal limits Creatinine clearance < 60 mL/min Uncontrolled bacterial or fungal infection at the time of enrollment Requirement for vasopressor support at the time of enrollment Karnofsky index <30% Pregnancy Somatic or psychiatric disorder making the patient unable to sign informed consent