Inclusion Criteria:

1. Clinical diagnosis of AML or ALL: CR2 or subsequent complete remission (CR) or CR1 with high-risk features or relapse with \< 10% blasts in BM and no circulating blasts.
2. Clinical diagnosis of CML: in CP1 (Chronic Phase 1) and resistant or intolerant to Gleevec or in CP2 or subsequent CP or in accelerated phase.
3. Clinical diagnosis of HD: induction failure or relapse and sensitive to last chemotherapy course.
4. Clinical diagnosis of NHL induction failure or relapse and sensitive to last chemotherapy course.
5. Clinical diagnosis of MDS with intermediate 2- or high-risk IPSS score.

Exclusion Criteria:

1. Less than twenty-one days have elapsed since the subject's last radiation or chemotherapy prior to conditioning (except Hydroxyurea).
2. HIV positive.
3. Pregnancy or lactation.
4. Uncontrolled bacterial, fungal or viral infection.
5. Subjects with signs and symptoms of active central nervous system (CNS) disease.
6. Availability of appropriate related and willing stem cell donor, who is HLA-matched at 5 or 6/6 antigens.
7. Prior allogeneic cell transplant.
8. Allergy to bovine or to any product, which may interfere with the treatment.
9. Enrolled in another clinical trial or received an investigational treatment during the last 30 days, unless approved by Sponsor.