A simple nonlinear global model with zonally symmetric forcing displays strong variability in its zonally averaged circulation on time-scales from weeks to months. These variations resemble the behavior of the zonal index in observations, especially in the Southern Hemisphere. In the model, as the zonal index varies, synoptic eddies and their associated fluxes follow the strongest westerlies poleward and equatorward. Synoptic fluxes of momentum sustain the index against dissipation, and are responsible for its persistence. While the momentum fluxes by low-frequency eddies are not well correlated with the index, they are significant in determining its tendency. DOI: 10.1034/j.1600-0870.1991.t01-4-00005.x