Abstract In chronic myeloid leukaemia (CML) allogeneic stem cell transplantation can be proposed to a minority of patients who are both less than 50 years of age and have an HLA-identical donor. Recombinant alpha-interferon induces cytogenetic responses (and prolongation of survival) in only 25–40% of patients. Thus, alternative treatments need to be proposed. When performed in chronic phase with unmodified stem cells, autologous stem cell transplantation is followed by cytogenetic responses in about 40% of cases, and some data suggest that these responder patients could have a prolongation of survival. This now needs to be demonstrated prospectively. If so, further studies could be performed in order to define the best source of stem cells (purged or unpurged) to be used.