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The paper describes the experimental and simulation work recently carried out to investigate the effects of secondary air injection on the emission conversion in the exhaust after-treatment system of a S.I. automotive engine. The modeling of the 1D unsteady reacting flows in the complete exhaust system of a spark ignition engine, designed to satisfy the Euro IV limits, has been performed including the secondary air injection system, to predict the possible shortening of catalyst light-off time and the speed-up of the after-treatment system warm-up. The transport of chemical species with reactions in gas phase (post-oxidation of unburned HC in the exhaust manifold) and in solid phase (conversion of pollutants in the catalyst) with and without secondary air has been simulated by the 1D thermo-fluid dynamic model GASDYN, developed by the authors.