One hundred and twenty patients with HLA-mismatched donors will be included over 6 years at multiple centers across Belgium through the transplant committee of the Belgian Hematological Society. The conditioning regimen will consist of fludarabine and 2 Gy TBI, followed by the infusion of donor HSC. Patients will be randomized 1/1 in double-blind fashion to receive or not MSC (1.5-.3.0 x106/kg) from third-party (either haploidentical family members or unrelated volunteer) donors on day 0. Postgrafting immunosuppression will combine tacrolimus and MMF. Except for the collection, expansion and infusion of MSC, the clinical management of the patient will not differ from that of routine NM-HCT.