Self-sustained current oscillations due to impurity breakdown in n-type GaAs epitaxial layers are reported for various magnetic-field strengths and orientations of the field with respect to the direction of current. In all cases relaxation oscillations at the onset of breakdown and formation of a current filament in the postbreakdown regime are observed. A magnetic field normal to the epitaxial layer destabilizes the filament and causes multifrequency oscillations and chaotic fluctuations. On the other hand, if the magnetic field lies in the plane of the layer the filamentary current flow is stable up to field strengths of 2 T.