A mathematical model of a catalytic converter for automobile diesel engines that contains zeolites for adsorption of hydrocarbons has been developed. The model includes a description of mass- and heat-transfer resistance at the external surface of the monolith washcoat and internal diffusion within the catalytic washcoat layer. Kinetic parameters for adsorption and oxidation of hydrocarbons [propene (C3H6), decane (C10H22), and toluene (C6H5CH3)], CO oxidation, and NOx adsorption and reduction were evaluated on the basis of dynamic experiments. Model simulations of dynamic operation regimes illustrate the effects of the inlet flow rate, temperature and adsorption capacity on the light-off, integral conversions, and spatiotemporal concentration patterns in the monolith. The effects of varying the transport properties of the washcoat layer (effective diffusion coefficient) and washcoat thickness are also investigated.