This is a non-randomized, open-label, multi center study. A cycle of therapy is 5 consecutive days every 21 days for 6 or more cycles. Stage I will consist of a brief run-in period in which patients with BPDCN (previously untreated and previously treated) and AML (persistent/recurrent and previously untreated) will be treated with SL-401 at 3 dose levels. During Stage 2, two cohorts of BPDCN and AML patients will be treated at the maximum tolerated dose or maximum tested dose in which multiple dose-limiting toxicities are not observed (identified in Stage 1).