Inclusion Criteria:

          1. Patients aged 18-70 years of age are eligible.

          2. Eligible histologies include:

               -  B-cell, T-cell or NK-cell NHL refractory to frontline or salvage therapy defined
                  as failure to achieve complete or partial remission according to standard
                  criteria.

               -  Diffuse large B-cell lymphoma relapsing within 12 months of finishing a rituximab
                  containing first line chemotherapy regimen (regardless of response to salvage
                  chemotherapy)or with evidence of c-myc. Primary refractory NHL (regardless of
                  response to salvage chemotherapy).

               -  Hodgkin lymphoma which is chemorefractory after at least two prior therapies.

               -  Hodgkin and NHL in an untreated relapse.

               -  Transformed NHL or chronic lymphocytic leukemia undergoing Richter's
                  transformation (regardless of response to last chemotherapy). Patients with
                  chemosensitive relapsed NHLs or Hodgkin lymphoma, but considered ineligible for
                  curative therapy with autologous transplantation, because of (a) inability to
                  collect stem cells, (b) prior autografting, (c) presence of myelodysplasia or (d)
                  histology not considered curable with autografting in opinion of treating
                  physician will be eligible.

          3. All patients must have at least one suitable HLA-matched sibling or volunteer
             unrelated donor available (according to institutional guidelines). HLA typing should
             be performed at least at serological level for HLA-A, -B, and -C and at allele level
             for HLA-DRB1. One antigen or allele level mismatch will be permitted between the donor
             and the recipient; however each donor/recipient pair must match at HLA-DRB1 at allele
             level.

          4. Patient must be able to provide informed consent.

          5. Left ventricular ejection fraction ≥ 40%. No uncontrolled arrhythmias or uncontrolled
             New York Heart Association class III-IV heart failure.

          6. Bilirubin, aspartate aminotransferase (AST), and Alanine transaminase (ALT) ≤ 3 x
             normal; and absence of hepatic cirrhosis.

          7. Adequate renal function as defined by a serum creatinine clearance of ≥ 40% of normal
             calculated by Cockcroft-Gault equation.

          8. DLCO (diffusion capacity; corrected for hemoglobin) or forced expiratory volume (FEV1)
             ≥ 50% of predicted.

          9. Karnofsky performance status ≥ 70.

         10. A negative pregnancy test will be required for all women of child bearing potential.
             Breast feeding is not permitted.

        Exclusion Criteria:

          1. Patients eligible for potentially curative therapy with autologous transplantation.

          2. Patients with lymphoblastic lymphoma.

          3. Patients with positive human immunodeficiency virus (HIV) serology.

          4. Clinical evidence of uncontrolled bacterial, viral or fungal infection at the time of
             transplant conditioning.

          5. Prior allogeneic transplantation.