Participants will be randomized to SCH 727965 or a comparator drug (bortezomib for mantle cell lymphoma [MCL] or alemtuzumab for B cell chronic lymphocytic leukemia [B CLL]). Part 1 of the study will determine the activity of SCH 727965 treatment in participants with MCL and participants with B-CLL. Part 2 of the study will determine the activity of SCH 727965 treatment in participants who experienced disease progression after standard treatment with the comparator drug during Part 1.

Inclusion Criteria:

• Age >=18 years, either sex, any race.

• Eastern Cooperative Oncology group performance status of 0 or 1.

• Adequate hematologic, renal, and hepatic organ function and laboratory parameters.

• For subjects with MCL:

  • Diagnosis of MCL according to the World Health Organization (WHO) criteria.
  • Received at least one prior chemotherapeutic regimen, but no more than two regimens including stem cell transplantation..
  • Measurable or assessable disease by the Revised Response Criteria for Malignant Lymphoma.

• For subjects with B-CLL

  • Documented B-CLL according to the National Cancer Institute Working Group (NCI-WG) criteria.
  • Received at least one prior alkylating agent-based regimen and one fludarabine- or pentostatin-containing regimen, but must not have received more than two prior regimens.
  • Measurable or assessable disease by NCI-WG criteria.

Exclusion Criteria:

• Known central nervous system involvement of MCL or B-CLL.
• Previous treatment with SCH 727965 or other cyclin-dependent kinase inhibitors.
• For MCL, previous treatment with bortezomib.
• For B-CLL, previous treatment with alemtuzumab.
• Known HIV infection.
• Known active hepatitis B or C.