The Yukawa coupling of the Higgs boson to the top quark is a key parameter of the Standard Model. It can be constrained using the associated production process pp → ttH + X. A search for this process using final states with multiple leptons, primarily targeting the decays H→ WW∗ and H → ττ, has been performed using the data set recorded by the ATLAS detector in 2015 and 2016 at a center of mass energy √s= 13 TeV. The analysis presented here includes two of the four final states distinguished by the number and flavor of leptons: two same-charge light leptons ( e or µ ) and no hadronically-decaying τ lepton candidates (2l0τhad) and four light leptons (4l), the remaining channels not covered being two same-charge light leptons and one hadronically-decaying τ lepton candidate (2l1τhad) and three light leptons (3l). The different background sources are also presented for each channel considered. The latest best-fit value for the ratio of observed versus