Subthalamic nucleus, internal globus pallidus and external globus pallidus are three important nuclei of the basal ganglia. A neuron population model of their interactions was established and its complex dynamical behaviors were investigated. Under the influence of appropriate external input, the system can switch between states of high and low frequency activity. Increasing striatal inhibition of the GP induces the generation of synchronized oscillations repeated at a low rate. The results indicate these dynamical behaviours, arising from the system, have important consequences for basal ganglia function.