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 .