The use of peripheral blood stem cells (PBSC) for allogeneic transplantation (PBSCT) is increasing steadily so that it cannot be considered an experimental practice any longer. Collection of PBSC requires the treatment of donors with G-CSF. With this drug, 10 to 16 mg/kg/day, side-effects are acceptable, but thrombocytopenia may follow the PBSC harvest. After transplant, allogenic PBSC engraft quickly in comparison with marrow. This has been shown for platelets, and to a lesser extent for granulocytes. Stability of graft has been documented by DNA analysis. With PBSC a high number of T- and NK-cells is infused, with a possible increase of GVL effect. However, we only have experimental evidence in the mouse that this may be the case. Incidence of acute GVHD equals that after BMT, but data on chronic GVHD are controversial, with an increased incidence reported in some studies. There is currently no indication for T-cell depletion of PBSC in HLA-identical sibling pair transplants. Experiments with CD34+ cell selection have sometimes produced a paradoxical increase of acute GVHD. The challenge of allogeneic PBSCT is improvement in survival, but available data only show that results are no worse than BMT. Prospective studies of allogeneic PBSCT versus bone marrow transplantation are in progress in Europe and USA.