The basal ganglia (BG) circuit, together with the motor cortex and the thalamus, plays an essential role in voluntary movement. In Parkinson’s disease (PD) patients, these structures exhibit exaggerated oscillations in the beta frequencies (10-30 Hz), a phenomenon also observed in animal models of parkinsonism, namely rats and non-human primates (NHP). Several potential generation mechanisms explaining this oscillatory activity have been hypothesized in various theoretical models, but a consensus has yet to be reached. Moreover, the extensive literature characterizing these oscillations and their behavior in patients and animal models highlights slight but consistent differences between species, such as their frequency within the beta range and relative power in various BG nuclei. These findings raise the question whether the mechanism of generation for the abnormal oscillations could differ across species.We propose a computational approach to analyze the oscillatory dynamics possibly driven within BG circuits. The BG-thalamo-cortical network is studied first in a simplified rate model and then in a spiking neurons model strongly constrained by experimental anatomical and physiological data. This network contains several negative-feedback loops, which represent good candidates for the spontaneous generation of oscillations, and whose temporal properties determine the achievable frequencies. Analyzing the frequencies and properties of oscillations generated by the different loops, we confront the different mechanisms with available data about abnormal oscillatory activity across different species. Our results, together with the known characteristics of beta oscillations across species, suggest the possibility that abnormal beta oscillations may arise from different mechanisms in different species.