The LEV/ULEV emission standards pose challenging problems on automotive exhaust gas treatment. This increases the need for good catalytic converter models, which can be applied for control. A dynamic converter model was made on the basis of first principles, accounting for the accumulation of mass in the bulk gas phase, in pores of the washcoat and on the catalytic surface, as well as for the energy accumulation in the gas and solid phase. The basis for the model is the elementary step kinetics of the individual global reactions. The main purpose of the model is to describe the low temperature behavior of the converter, when the majority of the emissions occur. The light-off process is analyzed in detail with different inputs. The biggest improvement occurs when secondary air is injected in front of the converter. The converter model is also coupled with a simple SI engine model to investigate the dynamic behavior of the whole system.