Most patients relapsing with AML either fail to achieve second remission or have only brief remissions. Patients more than 60 years of age or having histories of antecedent hematological disorders, prior chemotherapy, or poor risk cytogenetics have generally only short remissions and as a group have two year survivals of less than 10%. Equally patients with myeloid blast crisis of CML often fail to achieve remission or have responses of only brief duration. Laboratory studies have shown that AML leukemic blasts may be induced in culture to differentiate into dendritic cells which in turn may be used activate autologous lymphocytes to acquire leukemia specific cytotoxicity. This trial will assess the feasibility of generation of dendritic cell activated lymphocytes, and toxicity and efficacy of these activated cells given after reinduction chemotherapy. Before this study begins some toxicity information will have been generated in a trial of similar cells given to CML patients.