Hybrid homogeneous-heterogeneous reactions can arise in catalytic reactions carried out at elevated temperatures. In this work, hybrid N2O decomposition is investigated at higher temperatures. Unsteady-state processes, such as the periodic flow reversal of fixed-bed reactors have a considerable impact on the way reaction behaviour develops within distributed systems. For the first time, we present a macrokinetic model that incorporates the influence of competing adsorption and desorption of the reactants on the catalyst, as well as the shift in the observed activation energy of the catalyst in the presence of NO. We show that NO can lead to a considerable change in behaviour of the hybrid reaction, which consequently results in different macroscopic reactor performance and demonstrate this phenomenon with the aid of selected bifurcation diagrams.