Two models of catalytic monolith reactor with diffusion in the washcoat are described, employing the nonstationary kinetics of CO and hydrocarbon oxidation, NOx reduction, and oxygen storage with 23 reaction steps. The first model describes the dynamic behavior in a short monolith (recirculation reactor or CSTR), and the second one is a spatially two-dimensional nonstationary model of the monolith with plug flow. The models are used to demonstrate the qualitative agreement between the observed nonlinear dynamics of CO oxidation, including hysteresis and periodic and period-doubled oscillations, and earlier experiments. The effects of transport parameters within the washcoat on the monolith lightoff and on the outlet conversions are simulated. Computed spatiotemporal concentration patterns of reaction intermediates within the washcoat layer are used to discuss the oxidation and reduction functions of the three-way-catalyst monolith.