We investigate a model for the treatment of wastewater in the activated sludge process. This process is based on the aeration of waste water with flocculating biological growth, followed by the separation of treated waste water from biological growth. Part of this growth is then wasted, and the remainder is returned to the system. The wastewater reactor is assumed to be well mixed, so the mathematical formulation for this process can be represented by a continuously stirred tank reactor with recycle. This system is analysed by combining steady-state analysis with path-following techniques. In practice, wastewater is treated by a sequence of tanks arranged in series. By considering the performance of one tank, our work here provides a benchmark for comparing the performances of multiple tanks.