Based on the method developed by Berezowski and Burghardt (1993) for analysing the bifurcation to oscillatory solutions, the effect of the reaction order on oscillatory destabilization of a catalyst pellet is studied. A linear analysis of the dynamics of the system enabled a relationship to be determined between the critical Lewis number (i.e. the value above which oscillations begin to manifest themselves) and the remaining parameters of the system (gamma, beta*, Theta(0)). The non-linear analysis fully confirmed the results of the linear approach. Making use of the non-linear model, an analytical relation was found between the parameters of the system that define the region over which oscillatory instabilities are possible. For reaction orders less than 1, allowance was made for the fact that the reaction may stop in the vicinity of the pellet centre. For the zeroth-order reaction full analytical formulae were derived.