 This will be an open label, multi-center study of up to 77 patients with CML in chronic, accelerated or blast phase who have developed resistance to or have failed previous treatment with Gleevec imatinib mesylate. Because these patients may still be sensitive to Gleevec, adding Homoharringtonine may restore a response to Gleevec or the combined treatment may promote a better response than using Gleevec alone. 