We constructed and studies an imitation model of Co oxidation reaction on platinum metals. The model takes into account oxygen dissociative adsorption, monomolecular adsorption and desorption of carbon monoxide, active oxygen transformation into a less active oxygen of the second type, adsorbed CO reaction with the two types of oxygen, and CO diffusion over the surface. We found that adsorbate coverages and reaction rate undergo self-oscillations attended by the autowave behavior of adsorbates on the surface. With respect to oxygen partial pressures the interval of oscillations splits into three parts: nonregular relaxation oscillations, regular oscillations, and chaos, when the period and amplitude of adsorbate concentration oscillations change stochastically. The model shows that nonuniform distribution of the less active second type oxygen on the surface and the difference in the orders of reagents adsorption kinetics is the reason of oscillations. We suggest as well the reasons for the autowaves formation and development on the catalyst surface.