High frequency stochastic resonance (SR) phenomena, associated with fluctuational transitions between coexisting periodic attractors, have been investigated experimentally in an electronic model of a single-well Duffing oscillator which is bistable in a nearly resonant field of frequency omegaF. It is shown that, with increasing noise intensity, the signal-to-noise ratio (SNR) for a signal due to a weak trial force of frequency Omega approximately equal to omegaF at first decreases, then increases, and finally decreases again at higher noise intensities: The behavior is similar to that observed previously for conventional (low-frequency) SR in systems with static bistable potentials. The stochastic enhancement of the SNR of an additional signal at the mirror-reflected frequency |Omega-2omegaF| has also been observed, in accordance with theoretical predictions. Relationships with phenomena in nonlinear optics are discussed.