Abstract: Mixing of 1.56 µm infrared radiation from two lasers in a high quality YBa₂Cu₃O_7-δ thin film, patterned to parallel strips, was demonstrated. A mixer bandwidth of 18 GHz, limited by the measurement system, was obtained. A model based on nonequilibrium electron heating gives a good fit to the data and predicts an intrinsic mixer bandwidth in excess of 100 GHz, operating in the whole infrared spectrum. Reduction of bolometric effects and ways to decrease the conversion loss of the mixer is discussed. The minimum conversion loss is expected to be ~10 dB.