In 1983 IAWPRC formed a task group to facilitate the application of practical models to the design and operation of biological wastewater treatment systems. This paper presents an outline of the model developed for single-sludge systems performing carbon oxidation, nitrification and denitrification. The model includes seven fundamental processes: aerobic growth of heterotrophic biomass, anoxic growth of heterotrophic biomass, aerobic growth of autotrophic biomass, decay of heterotrophic biomass, decay of autotrophic biomass, hydrolysis of entrapped particulate organic matter, and hydrolysis of entrapped organic nitrogen. The model is presented in the form of a matrix which utilizes stoichiometric coefficients to couple the components in the model with the process rate expressions acting upon them.