Inclusion Criteria:

          -  Diagnosis of one of the following:

               -  Patients >= 60 years of age with previously untreated Ph-positive ALL (either
                  t(9;22) and/or BCR-ABL positive) (includes patients initiated on first course of
                  therapy before cytogenetics known) or with lymphoid accelerated or blast phase
                  chronic myelogenous leukemia (CML). These patients could have received one or two
                  courses of chemotherapy with or without other tyrosine kinase inhibitors (TKIs)
                  and still eligible. Patients < 60 years of age may be enrolled if they are
                  considered unfit for intensive chemotherapy: i) if they achieved CR, they are
                  assessable only for event-free and overall survival; OR ii) If they failed to
                  achieve CR, they are assessable for CR, event-free, and overall survival;

               -  Patients >= 18 years of age with relapsed / refractory Ph-positive ALL or with
                  previously treated lymphoid accelerated or blast phase CML.

          -  Performance status =< 2 (Eastern Cooperative Oncology Group [ECOG] scale).

          -  Total serum bilirubin =< 2 x upper limit of normal (ULN), unless due to Gilbert's
             syndrome (unless the increased values are judged to be leukemia disease related).

          -  Alanine aminotransferase (ALT) =< 3 x ULN (unless the increased values are judged to
             be leukemia disease related).

          -  Aspartate aminotransferase (AST) =< 3 x ULN (unless the increased values are judged to
             be leukemia disease related).

          -  Serum lipase and amylase =< 1.5 x ULN.

          -  For females of childbearing potential, a negative urine pregnancy test must be
             documented.

          -  Female patients who: are postmenopausal for at least 1 year before the screening
             visit, OR are surgically sterile, OR If they are of childbearing potential, agree to
             practice 2 effective methods of contraception, at the same time, from the time of
             signing the informed consent through 4 months after the last dose of study drug, OR
             agree to completely abstain from heterosexual intercourse.

          -  Male patients, even if surgically sterilized (i.e., status post-vasectomy), who: agree
             to practice effective barrier contraception during the entire study treatment period
             and through 4 months after the last dose of study drug, OR agree to completely abstain
             from heterosexual intercourse.

          -  Adequate cardiac function as assessed clinically by history and physical examination.

          -  Signed informed consent.

        Exclusion Criteria:

          -  Active serious infection not controlled by oral or intravenous antibiotics.

          -  History of acute pancreatitis within 1 year of study or history of chronic
             pancreatitis.

          -  History of alcohol abuse.

          -  Uncontrolled hypertriglyceridemia (triglycerides > 450 mg/dL).

          -  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.

          -  Active grade III-V cardiac failure as defined by the New York Heart Association
             criteria.

          -  Uncontrolled, or active cardiovascular disease, specifically including, but not
             restricted to: myocardial infarction (MI), stroke, or revascularization within 3
             months; unstable angina or transient ischemic attack; congestive heart failure prior
             to enrollment, or left ventricular ejection fraction (LVEF) less than lower limit of
             normal per local institutional standards prior to enrollment; diagnosed or suspected
             congenital long QT syndrome; clinically significant atrial or ventricular arrhythmias
             (such as atrial fibrillation, ventricular tachycardia, ventricular fibrillation, or
             Torsades de pointes) as determined by the treating physician; prolonged corrected QT
             (QTc) interval on pre-entry electrocardiogram (> 470 msec) unless corrected after
             electrolyte replacement or approved by cardiologist. Significant venous or arterial
             thromboembolism including deep venous thrombosis or pulmonary embolism. Patients with
             a history of treated prior superficial or catheter associated will not be considered
             as significant embolism and after discussion with principal investigator (PI) will not
             be excluded from eligibility; uncontrolled hypertension (diastolic blood pressure > 90
             mmHg; systolic > 140 mmHg). Patients with hypertension should be under treatment on
             study entry to effect blood pressure control.

          -  Taking any medications or herbal supplements that are known to be strong inhibitors of
             CYP3A4 within at least 14 days or 5 half-lives before the first dose of ponatinib in
             patients with newly diagnosed only.

          -  History or presence of clinically relevant central nervous system (CNS) pathology such
             as epilepsy, childhood or adult seizure, paresis, aphasia, stroke, severe brain
             injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome,
             or psychosis. Patients with active CNS leukemia will be excluded.

          -  Current autoimmune disease or history of autoimmune disease with potential CNS
             involvement.

          -  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.

          -  Pregnant and lactating women will not be eligible; women of childbearing potential
             should have a negative urine 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.

          -  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).

          -  Patients with documented significant pleural or pericardial effusions unless they are
             thought to be secondary to their leukemia.