Inclusion Criteria:

1. Diagnosis of one of the following: Previously untreated Ph-positive ALL [either t(9;22) and/or bcr-abl positive] (includes patients initiated on first course of hyper-CVAD before cytogenetics known) These groups will be analyzed separately. After 1-2 courses of chemotherapy with or without imatinib mesylate (Gleevec) · If they achieved CR, they are assessable only for event-free and overall survival, or · If they failed to achieve CR, they are assessable for CR, event-free, and overall survival. Patients with relapsed Ph-positive ALL or lymphoid blast phase of CML.
2. Age greater than or equal to 18 years
3. ECOG performance status less than or equal to 2
4. Adequate liver function (bilirubin less than or equal to 3.0 mg/dl, unless considered due to tumor), and renal function (creatinine less than or equal to 3.0 mg/dl, unless considered due to tumor)
5. Adequate cardiac function as assessed clinically.
6. Signed informed consent

Exclusion Criteria:

1. Active serious infection not controlled by oral or intravenous antibiotics
2. Treatment with any investigational antileukemic agents or chemotherapy agents in the last 7 days before study entry, unless full recovery from side effects has occurred or patient has rapidly progressive disease judged to be life-threatening by the investigator
3. Active secondary malignancy other than skin cancer (e.g., basal cell carcinoma or squamous cell carcinoma) that in the investigator's opinion will shorten survival to less than 1 year
4. Active Grade III-V cardiac failure as defined by the New York Heart Association Criteria. Uncontrolled angina, or MI within 6 months. Diagnosed or suspected congenital long QT syndrome. Any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de pointes). Prolonged QTc interval on pre-entry electrocardiogram (> 470 msec). Patients currently taking drugs that are generally accepted to have a risk of causing Torsades de Pointes (unless these can be changed to acceptable alternatives)
5. Prior history of treatment with dasatinib
6. Pregnant and lactating women will not be eligible; women of childbearing potential should have a negative pregnancy test prior to entering on the study and be willing to practice methods of contraception. Women do not have childbearing potential if they have had a hysterectomy or are postmenopausal without menses for 12 months. In addition, men enrolled on this study should understand the risks to any sexual partner of childbearing potential and should practice an effective method of birth control.
7. History of significant bleeding disorder unrelated to cancer, including: · Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease) · Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies)
8. Patients with documented significant pleural or pericardial effusions unless they are thought to be secondary to their leukemia