  We performed two-dimensional non-linear hydrodynamical simulations of
two-component gravitating disks aimed at studying stability properties of these
systems. In agreement with previous analytical and numerical simulations, we
find that the cold gas component strongly affects the growth rates of the
unstable global spiral modes in the disk. Already a five percent admixture of
cold gas increases approximately two-fold the growth rate of the most unstable
global mode while a twenty percent gas admixture enhances the modal growth rate
by a factor of four. The local stability properties of a two-component disk
coupled by self-gravity are governed by a stability criterion similar to
Toomre's Q-parameter derived for one-component systems. Using numerical
simulations, we analyse the applicability of a two-component local stability
criterion for the analysis of the stability properties of global modes. The
comparison of non-linear simulations with the analytical stability criterion
shows that the two-component disks can be globally unstable while being stable
to the local perturbations. The minimum value of the local stability criterion
provides, however, a rough estimate of the global stability properties of
two-component systems. We find that two-component systems with a content of
cold gas of ten percent or less are globally stable, if the minimum value of
the stability parameter exceeds about 2.5.
