Inclusion Criteria:

1. Diagnosis of 1) AML (WHO classification definition of >/= 20% blasts), or 2) intermediate-2 or high-risk MDS (defined by the IPSS classification2).
2. Patients aged 15 to 65 years;
3. For the initial run-in phase of the study, patients with relapsed or refractory disease or patients with secondary untreated disease are eligible, however, these patients must not have had prior exposure to a histone deacetylase inhibitor, prior antecedent hematological disorder or secondary disease with complex cytogenetics.
4. For the actual phase II portion of the study: patients must be chemonaïve, i.e., not have received any chemotherapy (except hydrea) for AML or MDS. They may have received hypomethylating agents for prior MDS and transfusions, hematopoietic growth factors or vitamins. Temporary prior measures such as apheresis or hydrea are allowed;
5. In those patients that have received prior therapy, at least 2 weeks need to have elapsed before participating in this study. Treatment may start earlier if deemed in the best interest of the patient after discussion with the PI of the study ;
6. ECOG performance status </= 2
7. Serum biochemical values with the following limits unless considered due to leukemia: creatinine </=2 mg/dl; total bilirubin </=2 mg/dL, unless increase is due to hemolysis or congenital disorder; transaminases (SG PT or SGOT) </=2.5x ULN;
8. Ability to swallow oral medication;
9. Ability to understand and provide signed informed consent;
10. Cardiac ejection fraction must be >/=50% (by either MUGA scan or echocardiography).

Exclusion Criteria:

1. Diagnosis of acute promyelocytic leukemia;
2. Active, uncontrolled, systemic infection considered opportunistic, life threatening or clinical significant at the time of treatment, or any severe concurrent disease, which in the opinion of the investigator and after discussion with the principal investigator, would make the patient inappropriate for study entry;
3. Male and female patients who are fertile agree to use an effective barrier method of birth control (i.e., latex condom, diaphragm, cervical cap, etc.) to avoid pregnancy. Female patients need a negative serum or urine pregnancy test within 7 days of study enrollment (applies only if patient of childbearing potential. Non childbearing is defined as 1 year or more postmenopausal or surgically sterilized);
4. Symptomatic CNS involvement;
5. Patient is unable to take and/or tolerate oral medications on a continuous basis;
6. Patient has known human immunodeficiency virus (HIV) infection or known HIV-related malignancy;
7. Patient has active hepatitis B or C infection. Active disease is defined as elevated liver enzymes and/or clinical symptoms of hepatitis in addition to positive blood test for hepatitis surface antigen. In the absence of elevated liver enzymes and/or clinical symptoms, the blood test for hepatitis core antigens is not required.
8. Patient is pregnant or breast-feeding;
9. Patient has a known allergy or hypersensitivity to any component of vorinostat;
10. Patient has a history of thrombotic disorders;
11. History of any psychiatric condition that might impair the patient's ability to understand or to comply with the requirements of the study or to provide informed consent.