A measurement of the tt¯ Z and tt¯ W production cross sections in final states with either two same-charge muons, or three or four leptons (electrons or muons) is presented. The analysis uses a data sample of proton–proton collisions at s=13 TeV recorded with the ATLAS detector at the Large Hadron Collider in 2015, corresponding to a total integrated luminosity of 3.2 fb- 1. The inclusive cross sections are extracted using likelihood fits to signal and control regions, resulting in σt t¯ Z= 0.9 ± 0.3 pb and σt t¯ W= 1.5 ± 0.8 pb, in agreement with the Standard Model predictions. © 2017, CERN for the benefit of the ATLAS collaboration.