Cord Blood Fucosylation

Inclusion Criteria:

1. Patients must have one of the following hematologic malignancies: a. Acute Myelogenous Leukemia (AML), Myelodysplastic Syndrome (MDS): high-risk for relapse first remission (with intermediate-risk or high-risk cytogenetics, flt3 mutation positive and/or evidence of minimal residual disease by flow cytometry), secondary leukemia from prior chemotherapy and/or arising from MDS, Langerhan's cell histiocytosis, second or third complete remission, or second relapse. b. Acute Lymphoblastic Leukemia (ALL): first complete remission with Philadelphia chromosome or translocation 4;11, hypodiploidy, and/or evidence of minimal residual disease by flow cytometry; second or third complete remission, or second relapse; secondary leukemia from prior chemotherapy. c. CML second chronic phase or accelerated phase. d. Non-Hodgkin's Lymphoma (NHL): second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant).
2. # 1, continued: e. Hodgkin's Disease (HD): second or third complete remission,or relapse (including relapse post autologous hematopoietic stem cell transplant). f. Chronic Lymphocytic Leukemia (CLL): Progressive disease following standard therapy.
3. Patients Age Criteria: Age >/= 1 and </= 80 years old. Eligibility for pediatric patients will be determined in conjunction with an MDACC pediatrician.
4. Performance score of at least 80% by Karnofsky or PS < 3 (ECOG) (age >/= 12 years), or Lansky Play-Performance Scale of at least 60% or greater (age <12 years).
5. Adequate major organ system function as demonstrated by: a. Left ventricular ejection fraction of at least 40-45% b. Pulmonary function test (PFT) demonstrating a diffusion capacity of least 50% predicted. For children </= 7 years of age who are unable to perform PFT, oxygen saturation >/= 92% on room air by pulse oximetry. c. Creatinine < 1.6 mg/dL. d. SGPT/bilirubin </= to 2.0 x normal.
6. Negative Beta HCG test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization and willing to use an effective contraceptive measure while on study.
7. Patients must have two CB units available which are matched with the patient at 4, 5, or 6/6 HLA class I (serological) and II (molecular) antigens. Each cord must contain at least 1.5 x 10^7 total nucleated cells/Kg recipient body weight (pre-thaw).
8. Have identified a back up cells source in case of engraftment failure. The source can be autologous, related or unrelated.

Exclusion Criteria:

1. Patients with known history of HIV/AIDS.
2. Active CNS disease in patient with history of CNS malignancy.
3. Patients with chronic active hepatitis or cirrhosis. If positive hepatitis serology, the Study Chair may deem the patient eligible based on the results of liver biopsy.
4. Patients with uncontrolled serious medical condition such as persistent septicemia despite adequate antibiotic therapy, decompensated congestive heart failure despite cardiac medications or pulmonary insufficiency requiring intubation (excluding primary disease for which CB transplantation is proposed), or psychiatric condition that would limit informed consent.