In this paper, a mathematical model, which describes a continuous aerobic membrane bioreactor (MBR) for the treatment of different kinds of wastewater, is developed. Firstly, a black box model is developed and verified by comparing simulation results with experimental data. In a second step, two shortcut models of different complexity are developed and verified. Both shortcut models use the black box balancing as a basis. However, component balances of carbon and oxygen are modified in order to connect the degradation of pollutants to the supply of substrate and dissolved oxygen. Both models show an increasing degree of agreement with experimental data.