Dust particles in a plasma can be higWy charged, and can carry a proportion of the negative charge of the plasma. Even if this proportion is quite small, as in interstellar dusty clouds, it can have a large effect on hydromagnetic Alfvén waves propagating at frequencies well below the ion–cyclotron frequency. In particular, the right-hand circularly polarised mode experiences a cutoff due to the presence of the dust. We generalise previous work on Alfvén waves in dusty interstellar plasmas by considering the general dispersion relation for waves propagating at an arbitrary angle with respect to the magnetic field. Wave energy propagating at oblique angles to the magnetic field in an increasing density gradient can be very efficiently damped by the Alfvén resonance absorption process in a dusty plasma, and we consider this damping mechanism for waves in interstellar clouds.