This paper is devoted to the development of a low-dimensional kinetic model of CO oxidation on a metallic catalyst surface and theoretical study of arising nonlinear phenomena and relaxation oscillations of the reaction rate. Experimental results of studies on the adsorbed oxygen are presented and its significance in the CO oxidation mechanism on Ir catalyst is shown. We consider the conventional Langmuir-Hinshelwood mechanism of catalytic CO oxidation and take into account the possibility of a metallic surface modification during reaction due to the oxygen penetration into subsurface layers. We suggest that when the adsorbed oxygen concentration exceeds some critical value, a surface modification occurs and the reaction capability of adsorbed oxygen changes, so that the activation energy of the interaction between the adsorbed species sharply increases. Construction of bifurcation curves on the parametric plane (P-CO, P-O2) permits us to separate areas of CO and O-2 partial pressures, for which self-oscillations and/or multiplicity of steady states appear. This paper deals with parametric analysis of a new two-variable kinetic model of CO oxidation on Ir catalyst surface, but the approach developed is rather general and can be applied to studies of different catalytic reactions. (c) 2004 Elsevier B.V. All rights reserved.