We explore the potential of electron-photon colliders to measure funda
mental supersymmetry parameters via the processes e gamma --> (e) over
tilde<(chi)over tilde>(0) (selectron-neutralino) and e gamma --> <(up
silon)over tilde><(chi)over tilde>(-) (sneutrino-chargino). Given the
<(chi)over tilde>(0) and <(chi)over tilde>(-) masses from e(+)e(-) and
hadron collider studies, cross section ratios sigma(gamma(-))/sigma(g
amma(+)) for opposite photon helicities determine the <(upsilon)over t
ilde>(L), (e) over tilde(L) and (e) over tilde(R) masses, independent
of the sparticle branching fractions. The difference m(<(upsilon)over
tilde>L)(2)-m((e) over tilde L)(2) measures M(W)(2)cos2 beta in a mode
l-independent way. The (e) over tilde(L) and (e) over tilde(R) masses
test the universality of soft supersymmetry breaking scalar masses. Th
e cross section normalizations provide information about the gaugino m
ixing parameters. (C) 1998 Elsevier Science B.V.