The purpose of this clinical research study is to provide dasatinib treatment to patients with advanced chronic myelogenous leukemia (CML) or Philadelphia chromosome positive acute lymphoblastic leukemia (Ph+ ALL) who no longer can tolerate treatment with imatinib. The safety of the treatment will also be studied.

Inclusion Criteria:

• Diagnosis of accelerated phase or blast phase CML or Ph+ ALL
• Intolerant or resistant to imatinib mesylate
• 18 years of age or older
• ECOG performance 0-2 (greater than 50% of time out of bed)
• Adequate liver and kidney function

Exclusion Criteria:

• Pregnant or breastfeeding females
• History of significant cardiac disease
• History of significant bleeding disorder (not CML)
• Prisoners