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Recent advances in the field of numerical modeling of unsteady reacting flows in the exhaust system of s.i. engines are presented in the paper. In particular, it is shown that the integration of a suitable chemical and thermal model for the catalytic converter within a 1D fluid dynamic simulation code has allowed the prediction of the exhaust gas composition from the cylinder to the tailpipe outlet, considering its variation across the catalyst. The composition of the exhaust gas, discharged by the cylinder, is calculated by means of a two- zone combustion model, including emission sub-models. The catalytic converter is simulated by a 1D fluid dynamic and chemical approach, considering laminar flow in each tiny channel of the substrate and chemical reactions in the solid phase, within the wash-coat. The predicted reaction rates are used to determine the specie source terms to be included in the one-dimensional fluid dynamic conservation equations.