We study the occurrence of final states with only an electron-positron
pair and missing transverse momentum as a signal of supersymmetry in
photon-photon collisions. Suitable high-energy photon beams may be pro
vided at linear colliders by back-scattering laser beams on electron b
eams. The final states considered represent a typical signature for th
e production and decay of selectron and chargino pairs within the mini
mal supersymmetric standard model. We show that, away from the kinemat
ical threshold, selectrons produce this signal far more abundantly tha
n charginos. The standard model background is dominated by W-pair prod
uction. We propose a series of kinematical cuts which reduce this back
ground to an acceptable level. With a 1 TeV collider operated in the g
ammagamma mode, we find that interesting and complementary tests of su
persymmetric models can be performed for selectron masses up to 350 Ge
V.