BACKGROUND: Narcolepsy is a lifelong neurological disorder with onset commonly in childhood or adolescence. No drugs are indicated for cataplexy and excessive daytime sleepiness in paediatric patients with narcolepsy. Sodium oxybate is approved for use in adult patients with excessive daytime sleepiness or cataplexy, or both, in narcolepsy. We aimed to examine the safety and efficacy of sodium oxybate oral solution treatment in children and adolescents who have narcolepsy with cataplexy. METHODS: This was a prospective, double-blind, placebo-controlled, randomised-withdrawal, multisite study and open-label investigation done at 30 sites in five countries (USA, Finland, France, Italy, and the Netherlands). Eligible participants were aged 7-16 years at screening, had narcolepsy with cataplexy, and were either being treated with sodium oxybate or were sodium oxybate-naive at entry. Sodium oxybate-naive participants were titrated to an optimal dose. Participants were randomly assigned (1:1) with a dynamic randomisation algorithm to receive placebo or to remain on sodium oxybate for 2 weeks; they then entered an open-label sodium oxybate treatment period for a total study duration of up to 1 year. Random assignment to placebo was discontinued if early efficacy was shown in the preplanned interim analysis of the primary efficacy endpoint, which was change in weekly number of cataplexy attacks. Participants entering the study after the interim analysis would then be assigned to receive open-label sodium oxybate for 2 weeks. The primary analysis of efficacy and safety included data collected until the cutoff date of Feb 10, 2017. The efficacy population consisted of all participants randomly assigned to receive an intervention who completed at least 5 days of dosing in the double-blind treatment period, and the safety population consisted of all participants who took the study drug, including open-label sodium oxybate. This study is registered with ClinicalTrials.gov, number NCT02221869. FINDINGS: Between Oct 1, 2014, and Feb 10, 2017, we enrolled 106 participants, and 104 took the study drug (the safety population). 96 (92%) of these participants completed the stable-dose period, of whom 63 participants (the efficacy population) were randomly assigned to receive sodium oxybate (n=31) or placebo (n=32) for 2 weeks. A preplanned interim analysis of the primary endpoint showed efficacy (p=0·0002), resulting in discontinuation of the placebo arm following guidance from the data safety monitoring board; 33 participants then received sodium oxybate on an open-label basis during the double-blind period. Participants who were randomly assigned to receive placebo and who were withdrawn from sodium oxybate (32 [51%] of 63 patients) had increased weekly cataplexy attacks (median increase of 12·7 attacks per week [Q1, Q3=3·4, 19·8]) when compared with those randomly assigned to continue treatment with sodium oxybate (median increase of 0·3 attacks per week [-1·0, 2·5]; p<0·0001). Commonly reported (>5%) adverse events were enuresis (15 [21%] of 72 sodium oxybate-naive participants vs four [13%] of 32 participants taking sodium oxybate at study entry), nausea (16 [22%] vs two [6%]), vomiting (15 [21%] vs two [6%]), headache (13 [18%] vs four [13%]), decreased weight (11 [15%] vs one [3%]), decreased appetite (eight [11%] vs none), nasopharyngitis (seven [10%] vs none), and dizziness (five [7%] vs 1 [3%]). Two serious adverse events (one event of severe acute psychosis and one event of moderate suicidal ideation) were reported, and both were considered to be related to the study drug. There were no reported deaths. INTERPRETATION: These results support the clinical efficacy of sodium oxybate for the treatment of both excessive daytime sleepiness and cataplexy in narcolepsy in children. The safety profile of sodium oxybate was consistent with that observed in adult patients. FUNDING: Jazz Pharmaceuticals.