 - To be eligible as a recipient for this study, patients must have chronic myelocytic leukemia CML in chronic phase and be older than 60 years of age, have advanced myelodysplastic syndrome MDS and be over 60 years of age, have chronic lymphocytic leukemia CLL and be over 50 years of age, or have low grade lymphoma and be over 50 years of age. HLA typing of the recipients family will be used to identify potential donors. Please contact study nurse for additional eligibility criteria. Final eligibility will be determined by the health professionals conducting this clinical trial. 