This trial was conducted to determine the dose-limiting toxicities (DLTs) and maximum tolerated dose (MTD) of the first in class NEDD8-activating enzyme (NAE) inhibitor, pevonedistat, and to investigate pevonedistat pharmacokinetics and pharmacodynamics in patients with acute myeloid leukaemia (AML) and myelodysplastic syndromes (MDS). Pevonedistat was administered via a 60-min intravenous infusion on days 1, 3 and 5 (schedule A, n = 27), or days 1, 4, 8 and 11 (schedule B, n = 26) every 21-days. Dose escalation proceeded using a standard ‘3 + 3’ design. Responses were assessed according to published guidelines. The MTD for schedules A and B were 59 and 83 mg/m2, respectively. On schedule A, hepatotoxicity was dose limiting. Multi-organ failure (MOF) was dose limiting on schedule B. The overall complete (CR) and partial (PR) response rate in patients treated at or below the MTD was 17% (4/23, 2 CRs, 2 PRs) for schedule A and 10% (2/19, 2 PRs) for schedule B. Pevonedistat plasma concentrations peaked after infusion followed by elimination in a biphasic pattern. Pharmacodynamic studies of biological correlates of NAE inhibition demonstrated target-specific activity of pevonedistat. In conclusion, administration of the first-in-class agent, pevonedistat, was feasible in patients with MDS and AML and modest clinical activity was observed.