Acoustoelectric amplification, in the linear approximation, is considered for a system containing several types of carriers in the two limiting cases of fast and slow carrier equilibration. The pertinent expressions are first derived for a piezoelectric semiconductor and then expanded to the more practical case of a layered system containing one or more semiconducting layers coupled to a piezoelectric element. An experimental example is given in the form of a guided elastic plate wave in lead zirconate titanate coupled to a plate of near‐intrinsic Ge.