It is known that ion beams are capable of generating whistler waves that propagate parallel to the mean magnetic field B0. Such waves may have been observed both upstream of the Earth's bow shock and in the vicinity of comets. We extend previous analyses to include propagation oblique to BO. The instability is generated by the perpendicular component of free energy in the ions; which can arise either via a temperature anisotropy (T⊥/T∥≫1) or via a gyrating distribution. In the former case the generation of whistler waves is confined to a fairly narrow cone of propagation directions centered about parallel propagation; while in the latter case, the maximum growth of the instability can occur at fairly large obliquities (&THgr;≂50¿). ¿ American Geophysical Union 1988