Supersymmetric Signatures at an $e$$\gamma$ Collider

High energy electron-photon colliders provide unique opportunities for probing physics beyond the standard model. We have studied the experimental signatures for two supersymmetric scenarios, with the lightest supersymmetric particle (LSP) being either the lightest neutralino or the gravitino. In the ``neutralino LSP'' scenario favored by the minimal supersymmetric standard model (MSSM), it is found that some basic parameters of the model, $\mu$, $\tan\beta$, $M_1$ and $M_2$, may be uniquely determined from the outgoing electron energy spectrum without assuming high scale unification of the masses or couplings. In the ``gravitino LSP'' scenario which occurs naturally in models of low energy dynamical supersymmetry breaking, it is possible to have background-free signatures if the next-to-lightest supersymmetric particle (NLSP) has a long decay length. In cases that the NLSP decays quickly, ways to distinguish among the experimental signatures of the two scenarios and of the standard model (SM) background are discussed.