A nonlinear-optical conversion process in a dual-wavelength vertical-external-cavity surface-emitting laser that leads to the generation of difference-frequency radiation in the long-wavelength part of the mid-infrared range (similar to 17.7 mu m) is analyzed numerically. The nonlinear crystal of GaAs is incorporated in the output-coupler mirror and, at the same time, is placed in a Fabry-Perot cavity tuned to the difference frequency. It is shown that the dependence of the nonlinear-conversion efficiency on the GaAs crystal thickness exhibits a pronounced resonance behavior and that the peak power of the radiation in the mid-infrared range can be as high as a few milliwatts with the parameters of the laser and the optical pump readily attainable experimentally.