  Conditions for the fragmentation of expanding shells due to gravitational
instability are discussed. The self-similar analytical solution is compared
with the results of 3-dimensional computer simulations for the expansion into
homogeneous media. For realistic galactic disks we show that the formation of
fragments is influenced by the amount of energy supply from the final number of
young stars in an OB association, the value of the sound speed, the
stratification and density of the ambient medium, the galactic differential
rotation and the gravitational force perpendicular to the galactic plane. The
typical size of gravitationally unstable shells is 1 kpc for an ambient gas
density n=1 cm^-3. In thick disk galaxies the fragmentation occurs in nearly
the whole shell while in thin disks it is restricted to the galactic equator.
Unstable fragments may become molecular and trigger the formation of molecular
clouds, and finally new star formation. We conclude that in dwarf galaxies the
star formation may propagate in all directions turning the system into a star-
burst. Contrary to that, the star formation in spiral galaxies propagates only
in some directions in a thin strip near the symmetry plane, basically at the
tips of the expanding shell.
