Doubly charged excited leptons give rise to interesting signatures for physics beyond the standard model at the present Large Hadron Collider. These exotic states are introduced in extended isospin multiplets which couple to the ordinary leptons and quarks either with gauge or contact effective interactions or a combination of both. In this paper we study the production and the corresponding signatures of doubly charged leptons at the forthcoming linear colliders and we focus on the electron-electron beam setting. In the framework of gauge interactions, the interference between the $t$ and $u$ channel is evaluated that has been neglected so far. A pure leptonic final state is considered ($e^{-} , e^{-} rightarrow e^{-} , e^{-} , u_{e} , bar{ u}_{e}$) that experimentally translates into a like-sign dilepton and missing transverse energy signature. We focus on the standard model irreducible background and we study the invariant like-sign dilepton mass distribution for both the signal and background processes. Finally, we provide the 3 and 5-sigma statistical significance exclusion curves in the model parameter space. We find that for a doubly charged lepton mass $m^*approx 2 $ TeV the expected lower bound on the compositeness scale at CLIC, $Lambda > 25$ TeV, is much stronger than the current lower bound from LHC ($Lambda > 5$ TeV) and remains highly competitive with the bounds expected from the run II of the LHC.
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