A search for the electroweak production of charginos and neutralinos decaying into final states involving three electrons or muons is presented. The analysis is based on 36.1 fb^-1 of √s = 13TeV proton–proton collisions recorded by the ATLAS detector at the Large Hadron Collider. Scenarios considered are based on simplified models with the associated production of the next-to-lightest neutralino and the lightest chargino, followed by their decays into final states with leptons and the lightest neutralino via either sleptons or Standard Model gauge bosons. No significant deviations from Standard Model expectations are observed and stringent limits at 95% confidence level are placed on the masses of relevant supersymmetric particles. For a massless lightest neutralino, masses up to 1.13TeV are excluded for the associated production of the next-to-lightest neutralino and the lightest chargino, assuming slepton mediated decays, whereas for gauge-boson-mediated decays, masses up to 380 GeV are excluded.