After leukapheresis and other pre-transplant procedures have been completed, patients will be hospitalized for approximately 14 to 21 days. On Days 1 through 5 of hospitalization, patients will receive IV fludarabine and one of several possible dose levels of cyclophosphamide. On Days 3 through 5, patients will receive IV thymoglobulin to kill the T-cells that cause the damage from systemic sclerosis. On Day 8, patients will receive their own stem cells from the previous leukapheresis procedure. While in the hospital, patients will be monitored by daily blood collection and will not be discharged until their white blood cell counts return to a safe, stable level. Prior to discharge from the hospital, patients will undergo a second leukapheresis.