Continuation software has been used for bifurcation analysis of the lumped approximation (a short monolith, CSTR) of the three-way catalytic converter (TWC). A nonstationary TWC reaction scheme evaluated from dynamic experiments on Pt/Ce/gamma-Al2O3 has been employed in the model. Multiple steady states (hysteresis) and oscillations are predicted both for the CO oxidation submodel and the full TWC scheme (the CO and hydrocarbon oxidation and the NOx reduction) in a certain range of operation parameters. The autocatalytic loops are identified by reaction network analysis. The operation of the monolith is then simulated by spatially 2D mathematical model of TWC converter where the description of internal diffusion in the washcoat and axial heat conduction are included. Kinetic oscillations reflect in complex spatiotemporal patterns in the washcoat along the monolith. (C) 2004 Elsevier Ltd. All rights reserved.