  Ideal MHD provides an accurate description of low-frequency Alfv\'en waves in
fully ionized plasmas. However, higher frequency waves in many plasmas of the
solar atmosphere cannot be correctly described by ideal MHD and a more accurate
model is required. Here, we study the properties of small-amplitude
incompressible perturbations in both the low and the high frequency ranges in
plasmas composed of several ionized species. We use a multi-fluid approach and
take into account the effects of collisions between ions and the inclusion of
Hall's term in the induction equation. Through the analysis of the
corresponding dispersion relations and numerical simulations we check that at
high frequencies ions of different species are not as strongly coupled as in
the low frequency limit. Hence, they cannot be treated as a single fluid. In
addition, elastic collisions between the distinct ionized species are not
negligible for high frequency waves since an appreciable damping is obtained.
Furthermore, Coulomb collisions between ions remove the cyclotron resonances
and the strict cut-off regions that are present when collisions are not taken
into account. The implications of these results for the modelling of
high-frequency waves in solar plasmas are discussed.
