  We present cross sections for the production of the lightest supersymmetric
particle as a neutralino state in the minimal supersymmetric standard model at
electron-photon colliders. The lightest supersymmetric particle mass is taken
at a value of 30 GeV which is slightly higher than its lowest experimental
bound of 20 GeV, and the masses of the scalar electron are varied. We show
partial cross sections of the energy and angular distribution of the outgoing
electron for different values of the centre of mass energy. As a result we show
that electron-photon collider experiments could be quite sensitive to the
detection of supersymmetric particles.
