In spite of numerous reports of kinetic instabilities during CO oxidation on supported noble-metal catalysts, previous models of the catalytic converter typically employed explicit rate-expressions. Such oscillatory motions or bistable behavior occur at low temperatures and should affect the converter cold-start performance. In this work we incorporate an oscillatory elementary-step kinetic model of CO oxidation into the converter model and analyze its behavior. The kinetic model was suggested by Sales et al. (1982 Surface Science, 114, 381-394) and we modify the suggested parameters to assure that the steady-state rate is monotonically increasing with temperature. We draw typical bifurcation maps, in the temperature vs. P-CO plane, for the isothermal kinetic model, for the catalyst surface (the lumped problem) and for the whole reactor and analyze the various boundaries by means of phase plane analysis. The domain of oscillations in the catalyst problem is quite similar to that in the converter and is bound by Hopf and global-saddle-node bifurcations. The converter may exhibit either a stable steady behavior or an oscillatory motion. In typical oscillations, which may be periodic or chaotic, a hot domain enters the reactor exit and moves quickly upstream; the following extinction occurs almost simultaneously due to strong coupling by convection. New avenues of cold-starting the converter, which is an excitable system, by means of periodic local perturbations upstream that send fronts propagating downstream are also suggested. The analysis shows, however, that this approach is not advantageous due to the slow relaxation of the surface activity during CO oxidation.