  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 ($e^{-} \, e^{-} \rightarrow e^{-} \, e^{-} \, \nu_{e} \,
\bar{\nu}_{e}$) 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.
