  In models with low-energy supersymmetry breaking, it is well-known that
charged sleptons can be significantly lighter than the lightest neutralino,
with the gravitino and lighter stau being the lightest and next-to-lightest
supersymmetric particles respectively. We give analytical formulas for the
three-body decays of right-handed selectrons and smuons into final states
involving a tau, a stau, and an electron or muon, which are relevant in this
scenario. We find that the three-body decays dominate over much of the
parameter space, but the two-body decays into a lepton and a gravitino can
compete if the three-body phase space is small and the supersymmetry-breaking
scale (governing the two-body channel) is fairly low. We study this situation
quantitatively for typical gauge-mediated supersymmetry breaking model
parameters. The three-body decay lengths are possibly macroscopic, leading to
new unusual signals. We also analyze the final-state energy distributions, and
briefly assess the prospects for detecting these decays at CERN LEP2 and other
colliders.
