Transient simulations of the methane-air mixture combustion in a Perfectly Stirred Reactor (PSR) with global one-step and two-step, reduced (by directed relation graph method) and detailed chemical reaction mechanisms, have been conducted. The simulation conditions were carefully selected to observe the dynamic of a PSR with an oscillating residence time close to the extinction. The effect of the oscillation amplitude and frequency have been investigated over a wide range of values. The temperature response of the global and reduced mechanismhas been compared to that of the detailed reaction mechanisms, the GRI Mech 3.0. The discussion of results points out limits and problems associated with the adoption of global reaction mechanisms. The results of the comparison indicate that the adoption of a global mechanism is not adequate in order to obtain an accurate description of methane-air combustion in a PSR with an oscillating residence time. This comparison underlines that only a little benefit is added by the adoption of the selected two-step mechanism. Instead, the reduced mechanism shows an excellent agreement with the detailed reaction mechanism.