Participants with acute myelogenous leukemia (AML) will be randomized to SCH 727965 or gemtuzumab ozogamicin. All participants with acute lymphoblastic leukemia (ALL) will receive SCH 727965. Part 1 of the study will determine the activity of SCH 727965 treatment in participants with AML and participants with ALL. Part 2 of the study will determine the activity of SCH 727965 treatment in participants with AML who experienced disease progression after standard treatment with gemtuzumab ozogamicin during Part 1.

Inclusion Criteria:

• For participants with AML:

  • Age >=60 years, either sex, any race.
  • Diagnosis of CD33-positive AML by World Health Organization criteria.
  • Must be in first or second relapse, or have primary refractory or refractory disease at first salvage, and not be considered a candidate for transplant.
  • Acute promyelocytic leukemia who has relapsed following treatment with both all trans retinoic acid (tretinoin) and arsenic trioxide-based therapy is eligible.

• For participants with ALL:

  • Age >=18 years, either sex, any race.
  • Diagnosis of ALL by World Health Organization criteria.
  • Must be in first or second relapse, or have primary refractory or refractory disease at first salvage, and not be considered a candidate for potentially curative therapy.
  • Eastern Cooperative Oncology group performance status of 0 or 1.
  • Adequate hematologic, renal, and hepatic organ function and laboratory parameters.
  • Receiving treatment with hydroxyurea or leukapheresis to reduce elevated white blood cell count to <=30 x 10^9 is eligible, provided hydroxyurea and leukapheresis are discontinued at least 24 hours before initiation of study drug.

Exclusion Criteria:

• Known central nervous system leukemia.
• Previous hematopoietic stem cell transplantation.
• Previous treatment with SCH 727965 or other cyclin-dependent kinase inhibitors.
• For AML, previous treatment with gemtuzumab ozogamicin.
• Known HIV infection.
• Known active hepatitis B or C.