Charged dust grains can have a large effect on the dispersion characteristics of hydromagnetic Alfve´n and magnetoacoustic waves propagating at frequencies well below the ion-cyclotron frequency, even if the proportion of the total charge on the dust (usually negative) is quite small in space and astrophysical plasmas, such as cometary atmospheres and interstellar molecular clouds. The dust introduces a cutoff-resonance pair. A number of effects of the dust are considered here. Wave energy propagating at oblique angles to the magnetic field in an increasing density gradient can be very efficiently damped by resonance absorption processes in a dusty plasma. It is shown that, as well as the usual Alfve´n resonance, a low frequency dust-ion hybrid resonance also occurs. The effects of dust on the dispersion of surface waves in highly structured plasmas and damping due to dust charging may also play roles in such plasmas. ©2000 American Institute of Physics.