Statistical distributions, power spectra and susceptibilities of an all-optical bistable system subject to noise are considered. In the presence of an additional small periodic signal, a stochastic-resonance phenomenon for additive noise is found to occur, and has been investigated theoretically and experimentally. A new form of optical heterodyning related to stochastic resonance, in which two high-frequency signals (an input signal and a reference one) are applied to an all-optical bistable system, is reported. A noise-induced enhancement of the heterodyne signal has been investigated theoretically, by means of analogue electronic simulation and in experiments in which an optical system was driven by two modulated laser beams at different wavelengths.