  In order to identify the exact criteria for the formation of two-ring
structures in galaxies, we studied the issue of gravitational instability of
the corresponding structural vibration modes against the background of a
composite disk model [1-3], which has an exact nonlinear law of
nonstationarity. Nonstationary analogs of dispersion equations for the given
structural vibration modes of the model are derived and the results of their
analysis are obtained. A comparative analysis of the increments of
instabilities of ring-like oscillation modes is carried out to determine the
dependence of their characteristic times of manifestation on the main physical
parameters of the model.
