This open-label extension will have a Screening Phase of up to one week (during Week 17) when patients will be evaluated for eligibility, an Open-Label Treatment Phase of 12 weeks duration (Weeks 18-Week 30), and a Post-Treatment Follow-Up Phase of 6 weeks (ending at Week 36 or 6 weeks from the date of the last dose of epoetin alfa). All patients will receive a first dose of epoetin alfa 40,000 U SC every 6 weeks beginning with Week 18, a second dose at Week 24, and a third and final dose at Week 30. During the Treatment Phase, Hb will be measured weekly. Dosing will not be increased during the open-label extension. A six-week follow-up period is required after administration of the Week 30 dose for those patients receiving all 3 doses. If Hb falls below 10 g/dL at any time or if the patient requires a red blood cell (RBC) transfusion, the patient will be withdrawn from the open-label extension, and the Post-Treatment Follow-Up Phase will occur 6 weeks later.