1. Diagnosis of Ph+ chronic myelogenous leukemia (CML) in first chronic phase without a complete hematologic response after 3 months of Imatinib mesylate therapy, or >=35% Ph+ cells despite > 6 months of Imatinib mesylate treatment, or after disease progression from a complete or partial response. Any patient with accelerated phase or blast crisis who achieves a subsequent chronic phase is eligible. Patients must have an HLA matched related or unrelated donor or one antigen mismatched related donor.