Mathematical models used to represent the activated sludge process are examined; means of analysis and computation of the differences and similarities between models are investigated. Two digital computer programs have been developed. The first program, the Continuous Steady State Activated Sludge (CSSAS) is a steady state model of the conventional activated sludge process flexible enough to simulate any of the proposed models. The second digital program Fill and Draw Activated Sludge (FADAS) attempts to simulate the biological activity in a fill and draw bench experiment in which activated sludge is mixed with substrate in any proportions. The FADAS program which has not been validated will be useful in interpretation of bench scale fill-and-draw experiments. The CSSAS program represents the most complete state-of-the-art computational procedure for quasi-steady-state performance of the activated sludge process but some important questions relating to design and operation of the process remain unresolved. However, further experimentation should ultimately result in a thoroughly reliable design tool. (WRSIC-abstract)