  We study signatures of heavy Majorana neutrinos at e- gamma colliders. Since
these particles violate lepton number, they can give rise to the reactions e-
gamma -> W- W- e+ and e- gamma -> W+ mu- mu- nu. The Standard Model background
contains extra light neutrinos that escape detection, and can be reduced
significantly after imposing appropriate kinematical cuts. We analyze the
physics potential of an e- gamma collider, with centre of mass energies sqrt(s)
= 0.5--1 TeV and a total integrated luminosity of 100/fb, for detecting heavy
Majorana neutrinos with masses mN = 100--400 GeV. Assuming that heavy neutrinos
couple predominantly to one lepton flavour at a time, we find that 10 expected
background-free events can be established for |B_{eN}| >~ 4.6 x 10^{-3}.
Instead, if no signal is observed, this will imply that |B_{eN}| ~< 2.7 x
10^{-3} and |B_{\mu N}| ~< 0.05 at the 90% confidence level.
