The Green’s functions method, adjusted to bounded crystalline structures (PriM 9-23$^{th}$), is applied to obtain the phonon dispersion law in superlattices. The system of difference equations defining Green’s functions of displacement type for a superlattice motive is given. Poles of Green’s functions define phonon spectra. They can be determined by solving the secular equation. In general case and for different boundary parameters, this problem is solved numerically (Mathematica 4) and presented graphically (CorelDraw 9). The correlation with spectra of phonons in the corresponding unbounded and film-structures is established in the work. The crystalline systems with the basic motive (made up from 2 different ultrathin films with specific interconnections) periodically repeating itself along one direction normal to the connected motive boundaries are the superlattices.