The dynamic behaviour of the CO oxidation reaction over Pd(110) has been studied by means of kinetic Monte Carlo modelling. The influence of the internal parameters on the shapes of surface concentration waves obtained in simulations under the limited surface diffusion intensity conditions has been studied. The hysteresis in oscillatory behaviour has been found under step-by-step variation of oxygen partial pressure. Two different oscillatory regimes could exist at one and the same parameters of the reaction. The parameters of oscillations (amplitude, period and the shape of spatio-temporal patterns on the surface) depend on the kinetic prehistory of the system. The possibility for the appearance of the cellular and turbulent patterns, spiral, ring and stripe oxygen waves on the surface in the cases under study has been shown. (c) 2004 Elsevier B.V. All rights reserved.