Inclusion Criteria:

1. Diagnosis of previously untreated Ph-positive ALL or previously treated in CR after 1-2 courses of therapy or failure after one course of induction chemotherapy without imatinib mesylate.
2. Age > or = 15 years. Those < 15 years of age will be treated under compassionate IND.
3. Zubrod performance status < or = 2 (ECOG Scale, Appendix A).
4. Adequate liver function (bilirubin < or = to 3.0 mg/dl, unless considered due to tumor), and renal function (creatinine < or = to 3.0 mg/dl, unless considered due to tumor).
5. Adequate cardiac function as assessed clinically by physical examination.
6. Signed informed consent.

Exclusion Criteria:

1. Active serious infection not controlled by oral or intravenous antibiotics.
2. Treatment with investigational antileukemic agent 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 life-threatening.
3. Active secondary malignancy other than skin cancer (e.g. basal cell carcinoma or squamous cell carcinoma) than in investigator's opinion will shorten survival to less than 1 year.
4. History of Grade III/IV cardiac problems as defined by the New York Heart Association Criteria.
5. Prior history of treatment with imatinib mesylate.
6. Pregnancy or lactating in women of childbearing potential.