In this work, we analyze the nonlinear behavior of an activated sludge process (ASP). In an ASP, the wastewater stream is fed to an aerator which sustains an aerobic biochemical reaction. The effluent from the aerator is taken to a downstream settler. The overflow from the settler is clear and is withdrawn from the system while the underflow which is rich in biomass is recycled. The aerator and the settler are coupled through this recycle stream. The accumulation of the biomass in the system is prevented by periodic sludge withdrawal from the system and control of the concentration of the suspension in the aerator. Earlier efforts have considered the settler to be perfect and have considered the recycle ratio (ratio of recycle flow to fresh feed flow) "R" as a parameter. Our approach focuses on capturing the essential physics of the interaction between the aerator and the settler and views R as a state variable. In this work, we propose a simple model of the separator incorporating a minimum flux or the limiting flux condition in the model of the settler. This uniquely determines the recycle rate in contrast to earlier studies where the recycle rate was fixed as a parameter. We compare two modes of sludge withdrawal (i) from the aerator and (ii) from the settler. The nonlinear behavior of this system is analyzed, and we discuss the new features which arise due to the incorporation of the limiting flux condition. The system of equations governing the system behavior is a differential algebraic system. For the scheme of purging from the aerator, we observed that the recycle ratio is very sensitive to the variation of the sludge withdrawal fraction. The system exhibits isolas, which develop unstable steady-state branches giving complex behavior. Here, for low values of the sludge withdrawal fraction, the system has two steady-state branches and there is a region of no steady states in between. For high values of the sludge withdrawal fraction, it is shown that the system can admit as many as six steady states.