Using a sample of e + e annihilation events collected with the L3 detector at the Z resonance corresponding to an integrated luminosity of 137 pb 1 , we have searched for anomalous production of X nal states where X represents stable, weakly interacting particles and the photon energy is greater than 15 GeV. The sample of events found is consistent with Standard Model expectations. Upper limits are set on Z couplings, the neutrino magnetic moment, and the branching ratio for Z ! X.