  The saturation conditions for bending modes in inhomogeneous thin stellar
disks that follow from an analysis of the dispersion relation are compared with
those derived from $N$-body simulations. In the central regions of
inhomogeneous disks, the reserve of disk strength against the growth of bending
instability is smaller than that for a homogeneous layer. The spheroidal
component (a dark halo, a bulge) is shown to have a stabilizing effect. The
latter turns out to depend not only on the total mass of the spherical
component, but also on the degree of mass concentration toward the center. We
conclude that the presence of a compact (not necessarily massive) bulge in
spiral galaxies may prove to be enough to suppress the bending perturbations
that increase the disk thickness. This conclusion is corroborated by our
$N$-body simulations in which we simulated the evolution of almost equilibrium,
but unstable finite-thickness disks in the presence of spheroidal components.
The final disk thickness at the same total mass of the spherical component
(dark halo + bulge) has been found to be much smaller than that in the
simulations where a concentrated bulge is present.
