Calculations are presented for various mechanisms by which two‐wave and three‐wave mixing of far‐infrared and millimeter‐wave signals in high‐purity GaAs might occur. The emphasis is on low IF, about 1 MHz, as detected by photoconductivity. The energy dependence of the carrier‐energy relaxation time and the carrier‐recombination time is found to be important, but for three‐wave mixing, in addition, the hydrogenic donor levels allow mixing by means of photoexcitation and modulation of the level densities, followed by thermal ionization that carries the modulation to the carrier density and the photocurrent.