Allogeneic bone marrow transplantation is the only way to cure patients with Ph1+ chronic myeloid leukemia. It is commonly assumed that, in order to obtain a cure for the patients, the leukemic clone must be completely destroyed by the conditioning treatment and the donor's bone marrow must repopulate the hemopoietic niches leading to a "complete chimera". However, cytogenetic analyses, supported by molecular ones, indicate that Ph1+ cells, far from being completely destroyed by chemo-radiotherapy may persist for a long time, probably in the majority of the patients. As demonstrated by the outcome of patients receiving T-cell depleted marrow, immune mechanisms must be involved in controlling and progressively reducing the size of the residual leukemic clone. Furthermore, immunodulating therapeutic strategies, represented by cyclosporin-A discontinuation or alpha interferon treatment, may successfully reduce the Ph1+ cell population even after a full relapse.