Computer simulation of the dynamics of layered AlN/GaN superlattices is performed to elucidate the microscopic nature of the vibrational states corresponding to the strongest bands in the Raman spectra. Experimental Raman spectra are shown to consist of two groups of lines, one of which exhibits a two-mode behavior and the other shows a one-mode behavior as the relative layer thicknesses are varied. The results of computer simulation and calculations within the dielectric-continuum approximation suggest that the behavior of the observed vibrational modes is dictated by the degree of their localization and that the interlayer coupling is due to long-range dipole-dipole interactions. It is shown that the delocalized modes, which exhibit one-mode behavior, can be used as a sensitive probe of the structure and composition of superlattices.