Nonlinear electromagnetic wave propagation in a magnetised plasma with heavy impurities, in particular dust grains,
at frequencies below and of the order of the ion-cyclotron frequency
is considered. The presence of immobile dust grains leads
to a considerable change of the dispersion characteristics for Alfven waves
propagating along the uniform magnetic field, especially for small wavenumbers when two
modes with a relatively large frequency gap appear. We discuss the
consequences of this dispersion for the nonlinear properties of the waves.