This is a randomized (the treatment you receive will be assigned by chance), double-blind (neither physician nor patient knows the name of the assigned drug), placebo-controlled (comparison with patients that receive treatment without active ingredient), multicenter study of epoetin alfa in anemic patients who are diagnosed with myelodysplastic syndromes (MDS) according to protocol-specified criteria. This study includes a 3-week prerandomization phase, a 24-week treatment phase and a 24-week treatment extension phase. All patients enrolled in the study will complete an end-of-study visit 4 weeks after the last dose of study drug (Week 28 or Week 52), or 4 weeks after early withdrawal (unless the reason for early withdrawal is withdrawal of consent). Between 125 and 159 patients will be enrolled in the treatment phase of the study. During the screening phase, which will take place within 2 weeks before starting study drug, the study doctor will do tests to see if the patient is suitable for this study. Patients meeting entry criteria for the study will then be randomly assigned to one of the 2 treatment groups. This means that each patient who is allowed to join the study is put into a group by chance, like flipping a coin. Group 1 patients will receive epoetin alfa 450 or increased up to 1050 International Units (IU) per kg body weight administered by subcutaneous injection (injection beneath the skin) using pre-filled syringes. Injections will be done once every week at a weight-based dose regimen (the total weekly dose received will depend on your weight) with a possible total maximum dose of 40,000 IU once every week for the first 8 weeks of the treatment phase and 80,000 IU once every week at any other time during the study. Group 2 patients will receive a matching volume of placebo administered once every week by subcutaneous injection. The chance that the patient will get epoetin alfa is 2 to 1. Doses of study drug will be withheld, decreased, or increased on the basis of erythroid response, weekly hemoglobin concentrations monitored in patients and predefined dose adjustment guidelines. Patients will see the study doctor every 4 weeks for a period of 24 weeks. At each visit the patient will undergo a full hematologic evaluation, serum chemistry evaluation, measurement of blood pressure and pulse rate, recording of blood product transfusions and transfusion complications, adverse events, concomitant therapies and an evaluation for disease progression. The patient's Erythroid response will be assessed at Week 8 and every 4 weeks thereafter, until Week 24. Blinded study treatment will be administered to all patients at Week 24. However, at the end of the treatment phase (after the Week 24 response assessment), only responders will enter the double-blind treatment extension phase to measure the duration of response. Patients will continue to receive the same treatment, in the same blinded fashion, and at the same dose as received at Week 24, and will return to the study center every 4 weeks, until Week 48, for assessment of the Erythroid response and the evaluations as described above. For all non-responders at Week 24 the treatment code will be broken after Week 28 assessments. For responders at Week 48, the treatment code will be broken after the Week 48 visit, following completion of the response assessment. The treatment code will not be broken for subjects who discontinue study treatment before Week 24, irrespective of whether they are responders or nonresponders. For these subjects, the blind will not be broken until all subjects have completed the study and the database is final. Once the patient stops receiving doses of study drug, he/she will be asked to see the study doctor for the safety follow-up visit, which is scheduled 4 weeks after the last dose of study drug. Safety will be monitored throughout the study at predetermined intervals and as clinically indicated by physical examination, laboratory tests and evaluation of adverse events. An Independent Data Monitoring Committee (IDMC) will periodically review study data and for the assessment of disease progression. The total duration of study participation will be for about 30 or 54 weeks.