Busulfan, Melphalan, and Fludarabine With Peri-transplant Palifermin, Followed by a T-Cell Depleted Hematopoietic Stem Cell Transplant From HLA Matched or Mismatched Related or Unrelated Donors in Patients With Advanced Myelodysplastic Syndromes (MDS) and Acute Myeloid Leukemia (AML)

Inclusion Criteria: * Patients should be \< 65 years. Patients \> or equal to 65 years will be accrued on a case by case basis after discussion and approval by the BMT Service. * Patients may be of either gender or any ethnic background. * Patients must have a Karnofsky or Lansky Performance Status \> or equal to 70%. * Patients must have adequate organ function measured by: \* Cardiac: asymptomatic or if symptomatic then LVEF at rest must be \> or equal to 50% and must improve with exercise. * Hepatic: \< 3x ULN ALT and \< 1.5 total serum bilirubin, unless there is congenital benign hyperbilirubinemia. * Renal: serum creatinine \< than or equal to 1.2 mg/dl or if serum creatinine is outside the normal range, then CrCl \> 60-ml/min/1.73 m2 * Pulmonary: asymptomatic or if symptomatic, DLCO \> 50% of predicted (corrected for hemoglobin) * Each patient must be willing to participate as a research subject and must sign an informed consent form. * Parent or legal guardians of patients who are minors will sign the informed consent form. Exclusion Criteria: * Active CNS or skin leukemic involvement * Female patients who are pregnant or breast-feeding * Active viral, bacterial or fungal infection * Patient seropositive for HIV-I/II; HTLV -I/II * Patients who have undergone a prior allogeneic or autologous stem cell transplant within the previous six months. * Patients who have had a previous malignancy that is not in remission.