We investigate theoretically the optical response of excitons localized near the surface of a semiconductor. Spectra of reflection of p-polarized light from strongly treated semiconductor surfaces are calculated by using a generalized Morse surface potential. The spectra exhibit prominent dips produced by the generation of exciton bound states and their corresponding longitudinal polariton modes. The position and the form of spectral dips depend not only on potential-well parameters but also on the value of the longitudinal-transverse splitting and the surface damping. Our results are compared with experimental spectra for CdSe and we also calculate reflectivity spectra for GaAs. \textcopyright{} 1996 The American Physical Society.