It is generally accepted that allogeneic stem cell transplantation can 'cure' chronic myelogenous leukemia (CML), although occasional patients relapse more than 10 years after the transplant procedure. Such cures presumably result from the combined effects of leukemia stem cells (LSCs) of the conditioning regimen and the graft-vs.-leukemia (GvL) effect mediated by donor-derived T lymphocytes. The advent of imatinib has revolutionized the management of patients with CML, but much evidence suggests that it does not eradicate all LSCs, which theoretically remain a potential source of relapse to chronic phase or advanced phase disease. Moreover, sub-clones of Philadelphia-positive cells bearing mutations that code for amino-acid substitutions in the Bcr-Abl kinase domain can be identified in patients receiving treatment with imatinib and are associated with varying degrees of resistance to this agent. In the present review, we postulate that LSCs, similar to their normal counterparts, may alternate between cycling and quiescent modes. In the cycling mode, they may express Bcr-Abl protein and be susceptible to the acquisition of additional mutations, whereas, in the quiescent mode, they may express little or no Bcr-Abl oncoprotein, cannot acquire additional mutations and are unaffected by imatinib. Thus, a patient who starts treatment early in the natural history of CML, and who responds to imatinib clinically, may not have had the opportunity to acquire additional mutations in LSCs. In this case, the persistence long-term of quiescent 'non-mutated' LSCs despite imatinib treatment might be consistent with freedom from relapse to chronic or advanced phase disease, provided that they remain vulnerable to imatinib when they are recruited into cycle. Conversely, when imatinib resistant Philadelphia-positive sub-clones predominate, this is likely to be due to the recruitment to hematopoiesis of quiescent stem cells that had been in cycle before administration of imatinib and that had acquired additional mutations; in such cases, the best approach to eradication of residual LSCs might be to target expressed proteins thought to be targets for the GvL effect.