We have derived a kinetic model for the propagation of low-frequency w
aves in a dusty plasma containing dust particles and drifting plasma p
articles. The model includes Landau damping or growth and damping from
charge variation on the dust particles, and is applied to dust-acoust
ic waves in planetary rings. Analytic expressions for the dispersion f
unction are used to examine the stability of this wave mode. The dispe
rsion properties are also found numerically for dense dust clouds or l
arge drift velocities, where the analytical expressions are not applic
able. We show how the stability condition depends on the density of du
st particles and the wavelength, for plasma and dust parameters which
may apply to Saturn's F ring, G ring, and E ring, and to Jupiter's rin
g.