The paper presents the fundamental elements of the multilevel mathematical models of heterogeneous catalytic reactors. These models are derived by means of the volume-averaging method, appropriately modified for the dispersed systems, and provide a theoretical basis for modelling heterogeneous systems across scales. The properties of the models are shown and analysed. A three-level model of a well-stirred catalytic reactor with bidispersed catalysts is presented. The model equations are solved by means of multilevel collocation. The transient behaviour of the reactor is investigated by means of computer simulation.