This is a Phase I, multi-center, open-label, dose escalation, MTD study of liposomal annamycin in children and young adults with refractory or relapsed ALL or AML. Enrollment will occur in cohorts of approximately 3 subjects with 10 additional subjects enrolled at the MTD. The liposomal annamycin doses will be escalated in sequential cohorts. Six dose levels of liposomal annamycin are planned: 130, 160, 190, 230, 280, and 310 mg/m2/day.