The periodic behaviour of a heterogeneous isothermal catalytic reactor involving a single irreversible reaction based on the Langmuir-Hinshelwood mechanism is studied. Square-wave concentration cycling of the reactants is used as the reactor input. The nonlinear behaviour of the reactor is analysed by using a special function developed in the present paper. The slope of this special function provides qualitative as well as quantitative information about the enhancement (ratio of periodic and steady-state performance) as a result of periodic operation for large cycle periods. Enhancement as a function of cycle period shows resonance behaviour for one special condition, i.e. for the products to be more strongly adsorbed than the reactants. Only this special condition is found to entail performance improvement over the optimum steady state. (C) 2003 Elsevier Ltd. All rights reserved.