An increase in beta-band frequency (13-30 Hz) activity has been observed in different nuclei of the basal ganglia (BG) of patients with Parkinson's disease (PD). However, recent studies have shown that beta oscillations are not only specific to pathological conditions. They have been shown to occur during sensorimotor tasks in healthy subjects. In this study, we used both a rate model and a spiking neural network to investigate the mechanisms responsible for the generations of beta oscillations. Results show that using a rate model with realistic time constants, the classical candidate - a recurrent network between the Subthalamic nucleus (STN) and external globus pallidus (GPe)- produces frequencies beyond the beta range and is consequently unlikely to be the main source of beta oscillations as previously suggested. We then propose two alternative circuits made of pallidostriatal feedback loops that can generate network oscillations in this range. Moreover, we show that with the pathophysiological changes due to dopamine depletion in PD, the network can transition from a steady-state where firing is asynchronous to a pathological state with synchronous oscillatory firing in beta-band frequencies. We explore how each of these loops behaves around the point of transition between the normal steady-state and the oscillatory regime depending on synaptic connection strengths. Finally, one by one, we add the aforementioned loops together and show that in a complete BG network we can reproduce the oscillatory behavior and phase-locking observed in Parkinsonian rats. Our results suggest that pathological oscillations are the product of the interactions between two or more feedback loops.