The paper presents the results of theoretical and experimental investigations of phonon polaritons at the free surface of the uniaxial single crystal A1,0, and for the three-layer structure "vacuum-uniaxial ZnO crystal-uniaxial A1,0,". The optical axes of the crystals are assumed to be normal to the interfaces of the media. The conditions of the existence of surface polaritons of different types are determined. It is shown that with the help of the attenuated total reflection technique (ATR) these polaritons could be used for the contactless determination of the film thickness as well as for nondamaging control of the main parameters of uniaxial crystals.