Test Extracorporeal Photopheresis (ECP) Treatment Before/After Allogeneic Bone Marrow Transplant (BMT) or Peripheral Blood Stem Cell (PBSC) Transplant to Prevent Graft Versus Host Disease

Inclusion Criteria: * Patients are eligible if they have a diagnosis of one of the following hematologic or lymphoproliferative malignancies for which a treatment option would be an allogeneic BMT or PBSC transplant: * acute myelogenous leukemia * chronic myelogenous leukemia * acute lymphocytic/blastic leukemia * chronic lymphocytic leukemia * myelodysplastic syndrome * non-Hodgkin's lymphoma (expected survival \> 60 days) * Hodgkin's disease (expected survival \> 60 days) * Patients who are candidates for a standard allogeneic BMT or patients who are candidates for a standard allogeneic PBSC transplant. * Patients must have a suitable HLA- molecular matched (8/10 or more) related or unrelated donor. * Patients must be physically and psychologically capable of undergoing a BMT or PBSC transplant and the attendant period of strict isolation. * Patients must test negative for human immunodeficiency virus (HIV). * Patients must present no evidence of active ongoing infection. * Patients must have adequate renal, hepatic, pulmonary, and cardiac function to enable the patient to tolerate the extracorporeal volume shifts associated with ECP, as determined by the physician's clinical judgment. * Platelets ≥ 20,000/cmm. * Patients ≥ 18 years of age. * Weight ≥ 40 kg (88 lb). * Systolic Blood Pressure ≥ 90 mm Hg after the patient has been in a sitting position for five minutes. * Women of childbearing potential must agree to use a reliable method of birth control for the duration of the study. * Patients must be willing to comply with all study procedures. * Signed and dated informed consent must be obtained prior to conducting any study procedures. The parent or legal guardian of a minor must also provide written informed consent. Exclusion Criteria * Patients who have received a prior allogeneic BMT or PBSC transplant. * Hypersensitivity or allergy to psoralen (methoxsalen). * Contraindication to radiation, cyclophosphamide, CSA, Busulphan or MTX. * Hypersensitivity or allergy to both heparin and citrate products. (If hypersensitive or allergic to only one of these two products, exclusion does not apply if the other product is strictly used for the patient.) * Patients whose treatment requires donor lymphocyte infusion up to day 100 post-transplant. * Participation in another clinical trial for prevention of GvHD within 7 days prior to patient enrollment or concurrent participation in any other clinical study. * Active gastrointestinal bleeding. * Females who are pregnant or lactating. * Previous treatment with ECP.