Signatures of Doubly Charged Higgs Bosons in e gamma Collisions

We study the discovery potential for doubly charged Higgs bosons, Delta^--, in the process e- gamma -> e+ mu- mu- for centre of mass energies appropriate to high energy e^+e^- linear colliders and the CLIC proposal. 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.