A quantum theory of acoustic parametric interaction in piezoelectric semiconductors is developed. The rate of acoustic sum frequency generation is expressed in terms of the nonlinear conductivity coefficient gamma , which is obtained for arbitrarily degenerate electron statistics by solving the equation of motion for the one-electron density operator to second order in the wave amplitudes. An anomalous variation of gamma is found to occur when the acoustic wavenumber becomes comparable with the characteristic electron wavenumber. This anomaly, which is associated with the cut-off of the linear acoustoelectric coupling, gives rise to an enhancement of the acoustic parametric interaction. In particular it becomes possible for acoustic sum frequency signals to be efficiently generated on the high-frequency side of the cut-off of the linear acoustoelectric coupling. Using X-ray diffraction techniques, this effect was observed in the piezoelectrically amplified sound flux of a highly doped GaAs single crystal.