Background: High-dose chemotherapy with haemopoietic stem-cell rescue improves event-free survival in patients with high-risk neuroblastoma; however, which regimen has the greatest patient benefit has not been established. We aimed to assess event-free survival after high-dose chemotherapy with busulfan and melphalan compared with carboplatin, etoposide, and melphalan. Methods: We did an international, randomised, multi-arm, open-label, phase 3 cooperative group clinical trial of patients with high-risk neuroblastoma at 128 institutions in 18 countries that included an open-label randomised arm in which high-dose chemotherapy regimens were compared. Patients (age 1-20 years) with neuroblastoma were eligible to be randomly assigned if they had completed a multidrug induction regimen (cisplatin, carboplatin, cyclophosphamide, vincristine, and etoposide with or without topotecan, vincristine, and doxorubicin) and achieved an adequate disease response. Patients were randomly assigned (1: 1) to busulfan and melphalan or to carboplatin, etoposide, and melphalan by minimisation, balancing age at diagnosis, stage, MYCN amplification, and national cooperative clinical group between groups. The busulfan and melphalan regimen comprised oral busulfan (150 mg/m(2) given on 4 days consecutively in four equal doses); after Nov 8, 2007, intravenous busulfan was given (0.8-1.2 mg/kg per dose for 16 doses according to patient weight). After 24 h, an intravenous melphalan dose (140 mg/m(2)) was given. Doses of busulfan and melphalan were modified according to bodyweight. The carboplatin, etoposide, and melphalan regimen consisted of carboplatin continuous infusion of area under the plasma concentration-time curve 4.1 mg/mL per min per day for 4 days, etoposide continuous infusion of 338 mg/m(2) per day for 4 days, and melphalan 70 mg/m(2) per day for 3 days, with doses for all three drugs modified according to bodyweight and glomerular filtration rate. Stem-cell rescue was given after the last dose of high-dose chemotherapy, at least 24 h after melphalan in patients who received busulfan and melphalan and at least 72 h after carboplatin etoposide, and melphalan. All patients received subsequent local radiotherapy to the primary tumour site followed by maintenance therapy. The primary endpoint was 3-year event-free survival, analysed by intention to treat. This trial is registered with ClinicalTrials. gov, number NCT01704716, and EudraCT, number 2006-001489-17. Findings: Between June 24, 2002, and Oct 8, 2010, 1347 patients were enrolled and 676 were eligible for random allocation, 598 (88%) of whom were randomly assigned: 296 to busulfan and melphalan and 302 to carboplatin, etoposide, and melphalan. Median follow-up was 7.2 years (IQR 5.3-9.2). At 3 years, 146 of 296 patients in the busulfan and melphalan group and 188 of 302 in the carboplatin, etoposide, and melphalan group had an event; 3-year event-free survival was 50% (95% CI 45-56) versus 38% (32-43; p= 0.0005). Nine patients in the busulfan and melphalan group and 11 in the carboplatin, etoposide, and melphalan group had died without relapse by 5 years. Severe life-threatening toxicities occurred in 13 (4%) patients who received busulfan and melphalan and 29 (10%) who received carboplatin, etoposide, and melphalan. The most frequent grade 3-4 adverse events were general condition (74 [26%] of 281 in the busulfan and melphalan group vs 103 [38%] of 270 in the carboplatin, etoposide, and melphalan group), infection (55 [19%] of 283 vs 74 [27%] of 271), and stomatitis (138 [49%] of 284 vs 162 [59%] of 273); 60 (22%) of 267 patients in the busulfan and melphalan group had Bearman grades 1-3 veno-occlusive disease versus 21 (9%) of 239 in the carboplatin, etoposide, and melphalan group. Interpretation: Busulfan and melphalan improved event-free survival in children with high-risk neuroblastoma with an adequate response to induction treatment and caused fewer severe adverse events than did carboplatin, etoposide, and melphalan. Busulfan and melphalan should thus be considered standard high-dose chemotherapy and ongoing randomised studies will continue to aim to optimise treatment for high-risk neuroblastoma.