This is an open-label (both the physician and the patient know which treatment is being provided), multi-center study of up to 16 weeks duration in which 450 patients will be randomly assigned (patients are assigned to a specific study group by chance) to one of three treatment groups in a 1:1:1 ratio. Patients will receive PROCRIT (epoetin alfa) 80,000 Units injected subcutaneously (under the skin) once every three weeks or 120,000 Units injected under the skin once every three weeks or ARANESP (darbepoetin alfa) 500 mcg injected under the skin once every three weeks for up to 13 weeks. PROCRIT (epoetin alfa) 80,000 Units and 120,000 Units given once every three weeks are doses and schedules that are not approved for use in the United States and are under investigation, while the ARANESP dose and schedule are approved for use in the United States. Adult patients with specific types of cancer (confirmed non-myeloid malignancy) who are scheduled to receive cyclic chemotherapy for a minimum of 12 weeks during the study and who meet all other eligibility criteria will be enrolled. This study will be conducted in approximately 80 study sites located in the United States.