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Basic knowledge about the reaction kinetics of the selective catalytic reduction (SCR) as well as measurement data from a dynamometer are used for the design of a physical mean-value model of an SCR catalytic converter system. The converter system consists of an injection device for urea solution and a coated metallic honeycomb-type converter. It is mounted in the tailpipe of a mobile, heavy-duty diesel engine. The core of the catalytic converter model is a series of identical SCR cells describing the thermal and chemical behavior of the SCR catalytic converter. It may be used to design dynamic, model-based feedforward controllers for the injection of reducing agent. Measurements on the dynamometer show that these controllers significantly improve the performance of the SCR system.