The activated sludge process is widely used to treat both municipal sewage and a variety of industrial wastewaters. We investigate the steady-state behaviour of an activated sludge process. We use the activated sludge model number one, an internationally accepted model, to describe the biochemical, biological, and physical-chemical phenomena that occur inside the bioreactor. The treatment configuration consists of a single aerated reactor attached to a settling unit. Continuation methods are used to determine the steady-states of the model as a function of the hydraulic residence time. From these solutions we construct important operational parameters including the chemical oxygen demand, total suspended solids and total nitrogen. These are determined inside the bioreactor, in the effluent stream and in the wastage stream. We show that there are two critical values of the hydraulic retention time. As the hydraulic retention time is increased through the first critical value heterotrophic biomass become viable. This bifurcation is associated with a substantial decrease in the chemical oxygen demand in the effluent stream and a corresponding increase in both the total suspended solids and total nitrogen in the reactor. Autotrophic biomass become viable as the hydraulic retention time is increased through the second bifurcation point. Associated with this bifurcation there are dramatic changes in the concentration of soluble ammonium nitrogen and soluble nitrate/nitrite inside the reactor; the former being converted to the latter. Of particular practical interest is the value of the hydraulic retention time at which the chemical oxygen demand in the effluent stream is equal to a preset target value. We investigate how this value varies as either the composition of the influent stream or the recycle ratio is varied.