Allogeneic transplantation of peripheral blood haematopoietic stem cells is gradually becoming an alternative to bone marrow transplantation (BMT), probably because of its convenience for the donor; i.e. the donor does not need to be hospitalised and there is less post-harvesting discomfort. Preliminary findings suggest that the two treatment modes do not differ in time to engraftment or the incidences of rejection and graft-versus-host disease. However, the effects of peripheral blood stem cell transplantation on long-term survival, duration of haematopoiesis, and clinical outcome in cases of unrelated donors with or without certain degrees of HLA mismatch remain to be established. Moreover, transplantation with umbilical cord blood, being rich in haematopoietic stem cells, is another alternative to BMT, particularly in small children.