BCR/ABL fusion tyrosine kinase transforms hematopoietic stem cells causing chronic myelogenous leukemia (CML) and acute lymphoblastic leukemia (ALL). BCR/ABL regulates numerous proteins involved in apoptosis, proliferation and cell – cell or cell – extracellular matrix interactions. However, BCR/ABL also enhances DNA damage caused by endogenous reactive oxygen species and exogenous genotoxic treatment. In addition, BCR/ABL modulates the response to DNA damage to promote genomic instability. This function leads to resistance to ABL kinase small molecular inhibitors (SMIs) imatinib (IM), dasatinib and nilotinib, and contributes to malignant progression of the disease. The former phenomenon is often caused by mutations in BCR/ABL kinase whereas the latter is associated with accumulation of additional genetic aberrations including chromosomal translocations, deletions, additional chromosomes, gene amplifications, and point mutations. Possible benefits of anti-mutagenic therapy used in pursuing the cure of BCR/ABL-positive leukemias are discussed.