In these last four decades there has been extraordinary progress in our understanding of the biology of, and therapeutic approach to, chronic myelogenous leukaemia (CML). During these decades new observations arising from studies of the biological behaviour of diploid and leukaemic stem cells and, recently, from clinical investigations have received the most attention. From a clinical point of view, allografting is still the only procedure which is able to cure CML. For patients without HLA-compatible donors, current therapeutic options include conventional chemotherapy (hydroxyurea), interferon-alpha (IFN-alpha) and autografting. While IFN-alpha (+/- low-dose ARA-C) must be considered the first-line therapy, autografting, according to our approach, or other procedures, raises the question of an ideal sequential strategy in the management of CML patients (diploid stem cell mobilization, autografting, IFN-alpha). Because it seems that the diploid haematopoietic reservoir declines with time, it may be desirable to mobilize and collect diploid stem cells in order to store them as soon as diagnosis is possible when the WBC count has been controlled by hydroxyurea.