Two realistic mathematical models were developed which can reproduce almost quantitatively the region of existence and the properties of the experimentally observed oscillatory behaviour for the N2O + H-2 and N2O + CO reactions over the Ir(110) single crystal surface. The peculiarity of the oscillatory behaviour in these systems is the phase shift between the oscillations of the partial pressures of the two reaction products. While the oscillation maximum for H2O is "delayed" compared to the maximum of N-2 oscillation, nearly anti-phase oscillations of the N-2 and CO2 production rates were observed. Moreover, not only the products N-2 and CO2 oscillate in counter-phase, but also the reactants N2O and CO produce counter-phase oscillations. It was demonstrated that in both systems oscillatory behaviour could originate due to the lateral interactions in the adsorbed layer. The main feedback mechanism generating oscillations operates via the acceleration of N2O decomposition by oxygen. The result of mathematical modeling shows that the larger phase shift of oscillations of CO2 and N-2 production rates in comparison with the H2O and N-2 production rates originates due to the more complicated character of lateral interactions in the adsorbed layer. (c) 2005 Elsevier B.V. All rights reserved.