In this paper we report molecular dynamics (MD) results for the surface dynamics of realistic model systems (krypton, lead). It turned out that the layers at the surface perform an unusual center-of-mass motion perpendicular to the surface; this new excitation should be due to the anharmonicities at the surface. The generalized phonon density of states has been studied in the bulk as well as at the surface of the crystal. The MD results are discussed in connection with dynamical-matrix solutions.