The kinetics of the catalytic reduction of NO by CO on Rh( 111) surfaces was investigated by using dynamic Monte Carlo simulations. Our model takes into account recent experimental findings and introduces relevant modifications to the classical reaction scheme, including an alternative pathway to produce N-2 through an (N-NO)* intermediate, the formation of atomic nitrogen islands in the adsorbed phase, and the influence of coadsorbed species on the dissociation of NO. All elementary steps are expressed as activated processes with temperature-dependent rates and realistic values dictated by experiments. Calculated steady-state phase diagrams are presented for the NO + CO reaction showing the windows for the conditions under which the reaction is viable. The model predicts variations in both production rates and adsorbate coverages with temperature consistent with experimental data. The effect of varying the individual kinetic parameters and the importance of each step in the reaction scheme were probed.