Supersymmetric Signals in $\gamma\gamma$ Collisions

We study the occurrence of final states with only an electron-positron pair and missing transverse momentum as a signal of \susy\ in photon-photon collisions. Suitable high energy photon beams may be provided at linear colliders by back-scattering laser beams on electron beams. The final states considered represent a typical signature for the production and decay of selctron and chargino pairs within the \mssm. We show that, away from the kinematical threshold, selctrons produce this signal far more abundantly than charginos. The standard model background is dominated by W-pair production. We propose a series of kinematical cuts which reduce this background to an acceptable level. With a 1 TeV collider operated in the $\gamma\gamma$-mode, we find that interesting and complementary tests of \susic\ models can be performed for selctron masses up to 350 GeV.