We present the results of cellular automaton and Monte Carlo simulations for the case of CO oxidation on a catalytic surface with simultaneous adsorption, reaction, and diffusion, including the Eley-Rideal step in the reaction mechanism. The results show that the carbon monoxide diffusion on the catalytic surface does not alter the qualitative nature of phase transitions. Also for any given adsorption to diffusion ratio the cellular automaton predicts slightly lower values of the phase transition point. The automaton has considerable speed advantage and corroborates the Monte Carlo simulation results. © 1998 American Chemical Society.