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.