Inclusion Criteria:

   - Subjects with hematologic malignancies (including myelodysplastic syndromes [MDS]) who
   are considered eligible for Cyclophosphamide (Cy)/Total Body Irradiation(TBI) +/-
   Etoposide (VP-16); Total Body Irradiation(TBI)/ Etoposide(VP-16); Melphalan(Mel) /
   Total Body Irradiation(TBI); Busulfan(Bu)/ Cyclophosphamide(Cy); Busulfan(Bu)/
   Melphalan (Mel); or Fludarabine(Flu)/ Melphalan(Mel) conditioning therapy with
   allogeneic stem cell support

   - Subjects with a 6/6 Human Leukocyte Antigen (HLA)-matched family member or unrelated
   donor who would provide donor marrow/ peripheral progenitor stem cells. [For unrelated
   matched donors, molecular typing of class I and class II is mandatory]

   - Karnofsky Performance Status >= 70%

   - 18 years of age or older at time of informed consent

   - Before any study-specific procedure, the appropriate written informed consent must be
   obtained

Exclusion Criteria:

   - Cancer other than Non-Hodgkin's lymphoma, Hodgkin's disease, acute myelogenous
   leukemia, acute lymphoblastic leukemia, chronic myelogenous leukemia, chronic
   lymphocytic leukemia, myelodysplastic syndrome or multiple myeloma (except: adequately
   treated basal cell carcinoma of the skin)

   - Prior autologous or allogeneic bone marrow or peripheral blood stem cell
   transplantation

   - Previous use of palifermin

   - Current active infection (including human immunodeficiency virus (HIV) and hepatitis)
   or oral mucositis

   - Congestive heart failure as defined by New York Heart Association class III or IV

   - Graft T-cell depletion for Graft-versus-host disease (GVHD) prophylaxis

   - Inadequate renal function (serum creatinine > 1.5x the upper limit of normal per the
   institutional guidelines or clearance < 40 ml/min adjusted for age)

   - Inadequate liver function (total bilirubin > 1.5x the upper limit of normal, aspartate
   aminotransferase (AST) > 3x upper limit of normal and/or alanine aminotransferase
   (ALT) > 3x upper limit of normal per the institutional guidelines)

   - Inadequate pulmonary function as measured by a corrected DLCO (diffusing capacity of
   the lung for carbon monoxide lung function test) <50% of predicted

   - Subject is currently enrolled in or has not yet completed at least 30 days since
   ending other investigational device or drug trial(s), or subject is receiving other
   investigational agent(s)

   - Subject of child-bearing potential is evidently pregnant (e.g. positive human
   chorionic gonadotropin- HCG test) or is breast feeding during Part A of the study

   - Subject or partner of subject is not using or refuses to use adequate contraceptive
   precautions during Part A of the study

   - Subject has known sensitivity to any of the products to be administered during dosing
   including Escherichia coli-derived products

   - Subject was previously randomized into this study

   - Subject will not be available for follow-up assessments

   - Subject has any kind of disorder that compromises the ability of the subject to give
   written informed consent and/or to comply with study procedures