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: $$H\rightarrow e\tau $$ , $$H\rightarrow \mu \tau $$ , and $$Z\rightarrow \mu \tau $$ . 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 $$\mathrm{fb}^{-1}$$ at a centre-of-mass energy of $$\sqrt{s}=8$$ TeV. No significant excess is observed, and upper limits on the lepton-flavour-violating branching ratios are set at the 95 $$\%$$ confidence level: Br $$(H\rightarrow e\tau )<1.04\%$$ , Br $$(H\rightarrow \mu \tau )<1.43\%$$ , and Br $$(Z\rightarrow \mu \tau )<1.69\times 10^{-5}$$ .