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The ATLAS detector at the Large Hadron Collider is used to search for excited electrons and excited muons in the channel \(pp →ℓℓ^\ast→ℓℓ\gamma \), assuming that excited leptons are produced via contact interactions. The analysis is based on \(13 fb^{−1}\) of pp collisions at a centre-of-mass energy of 8 TeV. No evidence for excited leptons is found, and a limit is set at the 95% credibility level on the cross section times branching ratio as a function of the excitedlepton mass \(m_{ℓ^\ast}\) . For \(m_{ℓ^\ast}\) ≽0.8 TeV, the respective upper limits on \(\sigma B(ℓ→ ℓ\gamma)\) are 0.75 and 0.90 fb for the \(e^\ast\) and \(μ^\ast\) searches. Limits on \(\sigma B\) are converted into lower bounds on the compositeness scale \(\Lambda\). In the special case where \(\Lambda = m_{ℓ^\ast}\), excited-electron and excited-muon masses below 2.2 TeV are excluded.