The properties of current-driven ion-acoustic (IA) and dust-acoustic (DA) modes in partially ionized plasmas are investigated. The current is oriented along the magnetic field lines and the mode is assumed to propagate at an angle with respect to the current. For highly collisional light plasma components, the fluid equations in the parallel direction are used. In the case of unmagnetized heavy species, which provide the mode inertia (ions for the IA mode and grains for the DA mode), the oblique perturbations will have an acoustic nature. For an arbitrary collision frequency of heavy species with neutrals, a kinetic description is used for the heavy species. For the DA mode, the dispersion equation is solved first in the limits of an electron-depleted plasma, showing that the mode has a minimum instability threshold at a large angle of propagation. This feature is primarily due to the collisions. For higher values of the charge on the grains, this minimum vanishes but the threshold becomes considerably lower. The full dispersion equation, with electrons having a current with an opposite sign compared to ions, is solved numerically yielding both a lower frequency and a smaller increment. A similar angle-dependent threshold and increment are found for the IA mode as well. (c) 2006 American Institute of Physics.