Basal ganglia are interconnected deep brain structures involved in movement generation. Their oscillations in the beta band (13-30Hz) is known to be linked to Parkinson's disease motor symptoms. In this paper, we provide conditions under which these oscillations may occur, by explicitly considering the role of the pedunculopontine nucleus (PPN). We analyze the existence of equilibria in the associated firing-rates dynamics , and study their stability by relying on a delayed MIMO frequency analysis. The results are illustrated by simulations.