Inclusion Criteria:

1. Patients with newly diagnosed AML or MDS (Intermediate 1 or higher risk)
2. Patient must have at least one of the following: a. Creatinine >/= 2 mg/dL; b. total Bilirubin >/= 2 mg/dL; c.ECOG Performance Status equal to 3 or 4; and d. is ineligible for participation on a protocol of higher priority
3. Patients must provide written informed consent.
4. Patients must be age > 18 years due to lack of safety information with these agents in children.
5. Patient agrees to: 1) Use 2 adequate methods of contraception to prevent pregnancy (either 2 barrier methods or a barrier method plus a hormonal contraceptive method) or 2) abstain from heterosexual activity throughout the study starting with Visit 1.
6. Female patients of childbearing potential should have a negative pregnancy test (serum) within 72 hrs. of study enrollment.

Exclusion Criteria:

1. Patients must not have the favorable cytogenetic abnormalities of inv (16), t (16;16), t (8;21), or t (15;17).
2. Patients receiving any anti-leukemic therapy with the exception of Hydroxyurea prior to study enrollment. Prior growth factor therapy is acceptable. Hydroxyurea could be used at the discretion of the treating physician.
3. Patient has a prior history of treatment with HDAC inhibitors. Patients who have received valproic acid (VPA) for the treatment of seizures may be enrolled on this study, but must not have received VPA within 30 days of study enrollment.
4. Patient is unable to take and/or tolerate oral medications on a continuous basis, examples include patients on a ventilator, or have altered mental status that precludes safe oral route of administration.
5. Patient has active hepatitis A, B, or C infection.
6. Patient is pregnant or breast-feeding.
7. Patient has a known allergy or hypersensitivity to any component of vorinostat or azacitidine.
8. 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.
9. Patient has a history of thrombotic disorders.