A simple model of the dynamics of a layered crystal having a hexagonal lattice with weak interaction of atoms in neighboring basal planes is formulated. Vibrations propagating in the basal plane with displacement vectors lying in the same plane are investigated. Energy–momentum relations are obtained for low-frequency (Rayleigh type) as well as high-frequency (gap-mode) vibrations localized at the free surface. The region of existence of quasi-surface phonons, whose boundaries are determined to a considerable extent by the shape of constant-frequency surfaces for two branches of bulk vibrations is determined. It is shown that peculiarities in the interaction of elastic waves with the crystal surface appear in the bulk spectrum at certain frequencies. The dispersion curves for surface vibrations separated from the continuous spectrum have a continuation in this spectrum in the form of dependences corresponding to transformation of a transverse wave into a longitudinal one. The effect of a surface monolayer of impurity atom on localized and pseudolocalized vibrations is investigated. ©1998 American Institute of Physics.