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.