Background: Phenytoin is the current standard of care for second-line treatment of paediatric convulsive status epilepticus after failure of first-line benzodiazepines, but is only effective in 60% of cases and is associated with considerable adverse effects. A newer anticonvulsant, levetiracetam, can be given more quickly, is potentially more efficacious, and has a more tolerable adverse effect profile. We aimed to determine whether phenytoin or levetiracetam is the superior second-line treatment for paediatric convulsive status epilepticus. Methods: ConSEPT was an open-label, multicentre, randomised controlled trial conducted in 13 emergency departments in Australia and New Zealand. Children aged between 3 months and 16 years, with convulsive status epilepticus that failed first-line benzodiazepine treatment, were randomly assigned (1:1) using a computer-generated permuted block (block sizes 2 and 4) randomisation sequence, stratified by site and age (≤5 years, >5 years), to receive 20 mg/kg phenytoin (intravenous or intraosseous infusion over 20 min) or 40 mg/kg levetiracetam (intravenous or intraosseous infusion over 5 min). The primary outcome was clinical cessation of seizure activity 5 min after the completion of infusion of the study drug. Analysis was by intention to treat. This trial is registered with the Australian and New Zealand Clinical Trials Registry, number ACTRN12615000129583. Findings: Between March 19, 2015, and Nov 29, 2017, 639 children presented to participating emergency departments with convulsive status epilepticus; 127 were missed, and 278 did not meet eligibility criteria. The parents of one child declined to give consent, leaving 233 children (114 assigned to phenytoin and 119 assigned to levetiracetam) in the intention-to-treat population. Clinical cessation of seizure activity 5 min after completion of infusion of study drug occurred in 68 (60%) patients in the phenytoin group and 60 (50%) patients in the levetiracetam group (risk difference −9·2% [95% CI −21·9 to 3·5]; p=0·16). One participant in the phenytoin group died at 27 days because of haemorrhagic encephalitis; this death was not thought to be due to the study drug. There were no other serious adverse events. Interpretation: Levetiracetam is not superior to phenytoin for second-line management of paediatric convulsive status epilepticus. Funding: Health Research Council of New Zealand, A+ Trust, Emergency Medicine Foundation, Townsville Hospital Private Practice Fund, Eric Ormond Baker Charitable Fund, and Princess Margaret Hospital Foundation.