The high content of immunocompetent T-cells in apheresis products may expose recipients of allogeneic peripheral blood stem cells (PBSC) to an elevated risk of acute and chronic graft-versus-host disease (GvHD). Thus, the use of an appropriate T-cell reduction or depletion technique might reduce this risk. The hazards of rejection and of a higher relapse rate should be avoided by maintaining a portion of the T-cells in the graft or by increasing the number of transplanted stem cells. The positive selection of CD34+ cells from peripheral blood preparations simultaneously provides an approximately 1,000-fold reduction of T-cells. Purified CD34+ cells containing committed and pluripotent stem cells are suitable for allogeneic transplantation. In transplantation from HLA-mismatched or three HLA-loci different family donors the amount of stem cells can be increased for reducing the incidence of rejection without increasing the T-cell number. In cases of poor marrow graft function a 'boost' with stem cells from the same family donor can be given. The risk of GvHD in transplantation from volunteer-matched unrelated donors might be reduced by T-cell depletion. If T-cells are used for enhancing the graft-versus-leukaemia effect, CD34+ enriched cells can be given for haematopoietic engraftment.