Propagation of electromagnetic surface waves in an infinite plasma layer is examined in kinetic approximation. The problem is solved with the Fourier method. The dispersion equation obtained is investigated (a) for high-frequency oscillations in which the average thermal velocity of the electrons υTe and of the ions υTi is much smaller than the phase velocity of wave VΦ; and (b) for low-frequency oscillations (ion-acoustic waves) in which υTe≫ VΦ≫ υTiFor high-frequency oscillations, wave damping is proportional to υTe, and not exponentially small as it is for a volume wave in an infinite plasma. As is known, damping of an ion-acoustic volume wave in an infinite plasma is caused by plasma electrons, and the ion contribution to damping is exponentially small if VΦ≪ υTi. In the case of an ion-acoustic surface wave, a large and sometimes even fundamental contribution to damping is made by plasma ions whose damping fraction is proportional to υTi. The reason for so large a damping in both high-frequency and low-frequency waves is Cerenkov absorption of the wave energy by plasma particles that is particularly considerable in the short-wave components of the Fourier expansion of the surface wave.