Inclusion Criteria:

          -  Adult patients aged ≤55 years (40< age ≤55 years);

          -  Patients who are candidates for myeloablative allogeneic bone marrow transplants: de
             novo or secondary acute lymphoblastic leukaemia (ALL) and acute myeloblastic leukaemia
             (AML) in complete remission (CR) ≥1; chronic myeloid leukaemia (CML) in chronic phase
             or in escape from tyrosine kinase inhibitors; myelodysplastic syndrome (MDS) with
             int-2 or high International Prognostic Scoring System (IPSS score, with medullary
             blastosis >10%); chemosensitive malignant non-Hodgkin's lymphoma (MNHL) in CR or
             partial remission (PR) >2 ; chemosensitive Hodgkin's disease in CR or PR >2 ;
             chemosensitive chronic lymphoid leukaemia (CLL) in CR or PR >2; chemosensitive myeloma
             in CR or PR ≥2;

          -  At high risk for GvHD: the risk for GvHD is considered high and the patient thus
             eligible for the study, if the receiver is >40 years, or if the donor is a woman and
             the receiver a man, regardless their age;

          -  Karnofsky index >70% or World Health Organization (WHO) index ≥2;

          -  Stable clinical conditions and life expectancy >3 months;

          -  Absence of organic disease contraindicating the transplantation

          -  Availability of a genotypically identical donor, aged >18 years, having given consent,
             and presenting no contraindications to bone marrow donation under general anaesthesia
             and to the required apheresis procedures;

          -  Written informed consent of the donor and patient.

        Exclusion Criteria:

          -  Age <40 years or > 55 years

          -  Organic disease contraindicating the utilisation of myeloablative conditioning

          -  History of allogeneic Hematological Stem Cell Transplantation (HSCT);

          -  History of autologous HSCT <1 year prior to the date for the scheduled allogeneic
             HSCT;

          -  Neurological location of the haemopathy justifying the transplantation;

          -  Pregnant or breastfeeding woman;

          -  Positive HIV serology;

          -  Positive hepatitis B or hepatitis C serology (except for post-vaccinal hepatitis B
             status);

          -  Absence of informed consent from the receiver or donor;

          -  Inability to adhere to the protocol instructions.