Young children have immature immune systems and respond poorly to standard influenza vaccines. The oil-in-water emulsion adjuvant MF59 can increase antigen uptake, macrophage recruitment, lymph node migration, and avidity to influenza virus. Therefore, we aimed to assess the relative efficacy, immunogenicity, and safety of an MF59-adjuvanted, quadrivalent, inactivated (subunit) influenza vaccine (aIIV4) compared with a US-licensed non-adjuvanted influenza vaccine in children. We did a multicentre, randomised controlled, observer-blinded, phase 3 trial of 146 sites including hospitals, clinics, and clinician offices in nine countries over two influenza seasons. We included children of either sex aged 6 months through 5 years. We stratified eligible participants and randomly assigned them (1:1), using a block size of four, to receive either aIIV4 or non-adjuvanted inactivated influenza vaccine (ie, trivalent inactivated influenza vaccine [IIV3] or quadrivalent inactivated influenza vaccine [IIV4]). We masked participants, parents or guardians, and outcome assessors to the administered vaccine. Designated personnel who were not masked administered aIIV4 in both seasons, or IIV3 in season one and IIV4 in season two. All vaccinations were administered intramuscularly. Children aged 6 through 35 months received one or two 0·25 mL doses, whereas those aged 3 through 5 years received one or two doses of 0·5 mL. The number of doses was dependent on previous vaccination status: vaccine-naive participants received a total of two doses of study vaccine, the first on day 1 and the second on day 29, whereas non-naive participants received only one dose on day 1. The primary outcome was relative vaccine efficacy assessed by RT-PCR-confirmed influenza due to any influenza strain in the overall study population and in prespecified age and dose subgroups. Immunogenicity against homologous and heterologous strains of influenza and safety were also measured. This study is registered with ClinicalTrials.gov, number NCT01964989. Between Nov 3, 2013, and March 5, 2014 (season one), and between Sept 30, 2014, and March 29, 2015 (season two), 10 644 participants were enrolled in this study. Of these participants, 10 612 were vaccinated (n=5338 with aIIV4 and n=5274 with comparator). Relative vaccine efficacy was not different between aIIV4 and the comparator vaccines in the overall study population (relative vaccine efficacy -0·67, 95% CI -19·81 to 15·41). The relative vaccine efficacy in the 6 through 23-month subgroup was significantly greater for aIIV4 than for the comparator vaccine (relative vaccine efficacy 31·37, 95% CI 3·14-51·38). aIIV4 elicited superior immunogenic response compared with the comparator for all four vaccine strains (geometric mean titre ratios 1·91 [95% CI 1·8-2·0] for A/H1N1, 1·71 [1·6-1·8] for A/H3N2, 2·19 [2·0-2·4] for B/Yamagata, and 2·27 [2·0-2·6] for B/Victoria) and three heterologous strains (1·94 [1·6-2·3] for A/H3N2, 2·17 [1·8-2·6] for B/Yamagata, and 2·12 [1·6-2·7] for B/Victoria) in participants aged 6 months through 5 years. The highest geometric mean titre ratios were observed in participants aged 6 through 23 months. Safety profiles were similar but more frequent solicited adverse events were reported with aIIV4 than with the comparator (3748 [73%] of 5138 vs 3242 [64%] of 5056). Although there was no additional benefit of aIIV4 compared with the US-licensed non-adjuvanted influenza vaccines in the overall study population, in the youngest and most vulnerable population of children in this trial, aIIV4 provided greater protection against influenza than a non-adjuvanted vaccine when assessed in this prespecified age group of 6 through 23 months. Additional clinical benefit was also apparent early after first vaccination in vaccine-naive participants aged 6 months through 5 years. Finally, aIIV4 and comparator had similar efficacy and vaccine safety profiles in children aged 6 months through 5 years. Seqirus UK Ltd.