Two basic versions of the acoustic deep-level transient spectroscopy (A-DLTS) technique based on the acoustoelectric effect resulting from the interaction between an acoustic wave and interfaces have been used to study deep centers in semiconductor structures. The former uses the high frequency transverse acoustoelectric signal (TAS) arising from the interaction of surface acoustic wave electric field and free carriers at the structure interfaces. The latter uses an acoustoelectric response signal (ARS) produced by the structure interface when a longitudinal acoustic wave propagates through the structure. An additional version of A-DLTS uses the acoustoelectric effect on light beam generated interface in high resistivity and along with photosensitive semiconductors. Planar Si MIS structure and GaAs/AlGaAs heterostructure capacitors and high resistivity GaAs were investigated by these versions of the A-DLTS technique. Several deep centers were found and their activation energies and corresponding cross-sections determined. Both the appearance of some A-DLTS peaks and the shift of practically all peaks of the A-DLTS spectra with increasing bias voltage in investigated structures can be considered to be the characteristic features of interface states. The polarization and the propagation direction of acoustic waves generated on the light beam produced interface appears as important condition of detected deep centers.