Direct searches for lepton flavour violation in decays of the Higgs and Z bosons with the ATLAS detector at the LHC are presented. The following three decays are considered: H→eτ, H→μτ, and Z→μτ. The searches are based on the data sample of proton–proton collisions collected by the ATLAS detector corresponding to an integrated luminosity of 20.3 fb−1 at a centre-of-mass energy of √s=8 TeV. No significant excess is observed, and upper limits on the lepton-flavour-violating branching ratios are set at the 95%% confidence level: Br(H→eτ)<1.04%, Br(H→μτ)<1.43%, and Br(Z→μτ)<1.69×10−5.