Spontaneous isothermal oscillations of N2O and O-2 outlet concentrations are observed in N2O decomposition on an over-exchanged Cu-ZSM5 catalyst. The oscillations are not chaotic but have a kinetic genesis. The oscillating behaviour is established over the pre-reduced catalyst after a transient phase whose duration is reduced with increasing the reactant inlet concentration. The addition of O-2 to the feed reduces the average N2O conversion and does not substantially affect the frequency and the amplitude of the oscillations up to an O-2/N2O inlet ratio equal to 10; only at higher inlet ratios do the oscillations disappear. Fourier analysis has revealed that the frequency of the oscillations increases by increasing either the feed flow rate or the N2O reactor inlet concentration. A reaction mechanism based on the periodic change of the copper oxidation state in the zeolite has been proposed. The mechanism allows us to explain most of the results obtained in different experimental conditions.