Mass balance equations for biomass and substrate are numerically solved to determine the effects of different variables on suspended growth systems. The longitudinal biomass gradient was taken into account. Monod kinetics and mathematical models of reactors-in-series are used to represent the actual conditions resulting from varying degrees of wastewater quality. An attempt has been made to determine the effluent concentration as a function of two parameters, ie a dimensionless time and a dimensionless substrate concentration of the incoming wastewater. Computer techniques are applied to express the results generally. By means of the numerical approach, the variation of the ratio between the hydraulic residence time of a given reactor and that of an equivalent plug-flow tank without longitudinal biomass gradient was investigated. Results were expressed in form of nomograms to characterize the plug-flow activated sludge systems and to provide the basis for design. Experimental data reported in the literature were also evaluated to demonstrate the cases where the existing classical solution to the problem differs from the exact results based upon Monod-type substrate removal. (C) 2000 Society of Chemical Industry.