Background: Several paediatric malignancies, including anaplastic large cell lymphoma (ALCL), inflammatory myofibroblastic tumour (IMT), neuroblastoma, and rhabdomyosarcoma, harbour activation of anaplastic lymphoma kinase (ALK) through different mechanisms. Here, we report the safety, pharmacokinetics, and efficacy of ceritinib in paediatric patients with ALK-positive malignancies. Methods: This multicentre, open-label, phase 1 trial was done at 23 academic hospitals in ten countries. Children (aged ≥12 months to <18 years) diagnosed with locally advanced or metastatic ALK-positive malignancies that had progressed despite standard therapy, or for which no effective standard therapy were available, were eligible. ALK-positive malignancies were defined as those with ALK rearrangement, amplification, point mutation, or in the case of rhabdomyosarcoma, expression in the absence of any genetic alteration. Eligible patients had evaluable or measurable disease as defined by either Response Evaluation Criteria in Solid Tumours, version 1.1 for patients with non-haematological malignancies, International Neuroblastoma Response Criteria scan for patients with neuroblastoma, or International Working Group criteria for patients with lymphoma. Other eligibility criteria were Karnofsky performance status score of at least 60% for patients older than 12 years or Lansky score of at least 50% for patients aged 12 years or younger. This study included a dose-escalation part, followed by a dose-expansion part, in which all patients received treatment at the recommended dose for expansion (RDE) established in the dose-escalation part. Both parts of the study were done in fasted and fed states. In the dose-escalation part, patients were treated with once-daily ceritinib orally, with dose adjusted for body-surface area, rounded to the nearest multiple of the 50 mg dose strength. The starting dose in the fasted state was 300 mg/m2 daily and for the fed state was 320 mg/m2 daily. The primary objective of this study was to establish the maximum tolerated dose (ie, RDE) of ceritinib in the fasted and fed states. The RDE was established on the basis of the incidence of dose-limiting toxicities in patients who completed a minimum of 21 days of treatment with safety assessments and at least 75% drug exposure, or who discontinued treatment earlier because of dose-limiting toxicity. Overall response rate (defined as the proportion of patients with a best overall response of complete response or partial response) was a secondary endpoint. Activity and safety analyses were done in all patients who received at least one dose of ceritinib. This trial is registered with ClinicalTrials.gov (NCT01742286) and is completed. Findings: Between Aug 28, 2013, and Oct 17, 2017, 83 children with ALK-positive malignancies were enrolled to the dose-escalation (n=40) and dose-expansion (n=43) groups. The RDE of ceritinib was established as 510 mg/m2 (fasted) and 500 mg/m2 (fed). 55 patients (30 with neuroblastoma, ten with IMT, eight with ALCL, and seven with other tumour types) were treated with ceritinib at the RDE (13 patients at 510 mg/m2 fasted and 42 patients at 500 mg/m2 fed). The median follow-up was 33·3 months (IQR 24·8–39·3) for patients with neuroblastoma, 33·2 months (27·9–35·9) for those with IMT, 34·0 months (21·9–46·4) for those with ALCL, and 27·5 months (22·4–36·9) for patients with other tumour types. An overall response was recorded in six (20%; 95% CI 8–39) of 30 patients with neuroblastoma, seven (70%; 33–93) of ten patients with IMT, six (75%; 35–97) of eight patients with ALCL, and one (14%; <1–58) of seven patients with other tumours. The safety profile of ceritinib was consistent with that observed in adult patients. All patients had at least one adverse event. Grade 3 or 4 adverse events occurred in 67 (81%) of 83 patients and were mostly increases in aminotransferases (alanine aminotransferase increase in 38 [46%] patients and aspartate aminotransferase increase in 27 [33%] patients). At least one serious adverse event was reported in 40 (48%) of 83 patients and 31 (37%) of 83 patients had at least one grade 3 or 4 serious adverse event. 14 (17%) deaths occurred during the study, of which 12 were on-treatment deaths and two were after 30 days of the last dose. Of the 12 on-treatment deaths, ten were due to disease progression (neuroblastoma), one due to sepsis, and one due to intractable hypotension. Interpretation: Ceritinib 500 mg/m2 once daily with food is the recommended dose for paediatric patients with ALK-positive malignancies. Ceritinib showed promising preliminary antitumour activity in patients with ALK-positive refractory or recurrent IMT or ALCL, and in a subset of patients with relapsed or refractory neuroblastoma, with a manageable safety profile. Our data support the notion that ALK inhibitors should be considered in therapeutic strategies for paediatric patients with malignancies with genetic ALK alterations. Funding: Novartis Pharmaceutical Corporation.