Sensitivity to Doubly Charged Higgs bosons in the Process e^- γ\ to e^+ μ^- μ^-

We study the sensitivity to doubly charged Higgs bosons, $\Delta^{--}$, in the process $e^-\gamma\to e^+ \mu^-\mu^-$ for centre of mass energies appropriate to future high energy $e^+e^-$ collider proposals. For $M_\Delta < \sqrt{s_{e\gamma}}$ discovery is likely for even relatively small values of the Yukawa coupling to leptons. However, even far above threshold, evidence for the $\Delta$ can be seen due to contributions from virtual intermediate $\Delta$'s although, in this case, $\mu^-\mu^-$ final states can only be produced in sufficient numbers for discovery for relatively large values of the Yukawa couplings.