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: $H\to e\tau$, $H\to\mu\tau$, and $Z\to\mu\tau$. 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 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$(H\to e\tau) <$ 1.04%, Br$(H\to\mu\tau) <$ 1.43%, and Br$(Z\to\mu\tau) <$ 1.69 $\times$ 10$^{-5}$.

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