  We examine the local stability of galactic discs against axisymmetric density
perturbations with special attention to the different dynamics of the stellar
and gaseous components. In particular the discs of the Milky Way and of NGC
6946 are studied. The Milky Way is shown to be stable, whereas the inner parts
of NGC 6946, a typical Sc galaxy from the Kennicutt (1989) sample, are
dynamically unstable. The ensuing dynamical evolution of the composite disc is
studied by numerical simulations. The evolution is so fierce that the stellar
disc heats up dynamically on a short time scale to such a degree, which seems
to contradict the morphological appearance of the galaxy. The star formation
rate required to cool the disc dynamically is estimated. Even if the star
formation rate in NGC 6946 is at present high enough to meet this requirement,
it is argued that the discs of Sc galaxies cannot sustain such a high star
formation rate for longer periods.
