This trial, sponsored by Amgen, Inc., which produces the recombinant methionyl human stem cell factor (r-metHuSCF), also involves two other institutions. The primary objective is determination of the safety of administering multiple doses of r-metHuSCF in the setting of acquired aplastic anemia and evaluation of the effect of r-metHuSCF on peripheral blood counts. Potential effects of r-metHuSCF on frequency of need for red cell or platelet transfusions and on bone marrow morphology/cellularity will also be evaluated.