Using a sample of e+e- annihilation events collected at the Z resonance corresponding to an integrated luminosity of 11.2 pb-1, we have searched for gammaX final states where X represents stable, weakly interacting particles and the energy of the photon is greater than 1/2 E(beam). No events were found. The results have been interpreted within a composite Z model and a supergravity model with a light gravitino.