Some observational data indicate that galaxy subsystems, including their central areas, first of all are the result of their global nonstationary evolution. That is why we earlier built (Nuritdinov 1992) the exact non-linearly pulsing rotating models of disklike and spherical self-gravitating systems. Unlike other authors we want to research the stability problem of nonlinear nonstationary models. In the present report we want to give only those results of the instability studied, which have a direct attitude to the subject under discussion. We put a certain question: what initial conditions have to exist, for instance, for the value of the virial parameter (2T/|U|)0 and the parameter of anisotropy < Tr > / < T⊥ >, that the collapse of a disk should result in a bar, and the spherical collapse will result in a thick ellipsoidal bulge. To answer the question it is very important to study stability of the solvable nonlinear unequilibrium models. All models discussed below pulsate under the law R = II(ψ)R0, where (Nuritdinov 1985)