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.The primary objectives of this study are 1) to evaluate the safety and identify the maximum tolerated dose (MTD) of liposomal annamycin when given in 3 consecutive daily doses, starting at 130 mg/m2/day and ranging to as high as 310 mg/m2/day, or the MTD, whichever is lower, in children and young adults with refractory or relapsed acute lymphocytic leukemia (ALL) or acute myelogenous leukemia (AML), and 2) to evaluate the antileukemic activity of liposomal annamycin in children and young adults with refractory or relapsed ALL or AML. The secondary objective is to measure the pharmacokinetics of annamycin and its metabolite, annamycinol.