Basal ganglia are interconnected deep brain structures involved in movement generation. Their persistent beta-band oscillations (13-30 Hz) are 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 analyse the existence of equilibria in the associated firing-rate dynamics and study their stability by relying on a delayed multiple-input/multiple-output (MIMO) frequency analysis. Our analysis suggests that the PPN has an influence on the generation of pathological beta-band oscillations. These results are illustrated by simulations that confirm numerically the analytic predictions of our two main theorems.