Structural and dynamic properties of short-period GaN/AlN superlattices with the thicknesses of the constituent layers varying from two to several monolayers, grown using the method of submonolayer digital molecular beam epitaxy, are experimentally and theoretically studied. It is established that in the grown samples there are two types of periodicity. One type is formed by periodic sequence of GaN and AlN layers in the superlattice, and the second one is related with periodic interruptions in the growth of superlattice for the evaporation of excess Ga metal. The dependences of the positions and intensities of the lines in the Raman spectra on the period of the superlattice are determined, and microscopic nature of optical phonon modes is established. The doublet structure of the E(TO) lines localized in the GaN and AlN layers of superlattice, genetically related to the E 2(high) and E1 phonon branches of the bulk crystal, is first discovered and explained. A strong dependence of the polar modes localized in the AlN layer on the thickness of layer forming the superlattice is revealed. The results of complex studies will improve the accuracy of quantitative estimation of important parameters of superlattice structures and can be used to optimize growth parameters for the fabrication of structurally perfect short-period GaN/AlN superlattices.