  We study the possible signature for lepton-flavor violation processes in the
scalar-lepton sector of the minimal supersymmetric model at future
electron-photon colliders. We find that an $\egm$ collider can provide a good
opportunity to probe the mass differences and flavor mixing angles between the
sleptons of the first generation and the other two generations for the
right-handed as well as the left-handed sector. The sensitivity reach for
lepton-flavor violation is comparable to that obtained at an $e^+e^-$ and
$e^-e^-$ collider, and is significantly better than the current bound from
low-energy rare processes such as $\mu \to e \gamma$.
