The design and testing of a control system for reverse-flow catalytic afterburners based on a two-variable bifurcation map is focused on. The combustion of lean methane-air mixtures is considered as the test reaction and a bench-scale apparatus, with a special temperature-control system based on dynamic compensation of the thermal losses to achieve adiabatic operation, is used for validation purposes. The aim of the control system is to avoid both catalyst overheating and reaction extinction when the adiabatic temperature increases and the flow rate of the feed changes. Stability maps of the reactor are obtained by means of numerical simulations, showing the values of the operating parameters (switching time), which allows fulfillment of the operating constraints (catalyst maximum temperature and methane conversion) when the inlet concentration and flow rate change. This system was realized and tested experimentally, mainly for inlet concentration changes, proving to be effective in all cases investigated. (c) 2005 American Institute of Chemical Engineers.