Periodic operation of several adiabatic fixed beds connected in series is an alternative to conventional steady-state fixed-bed operation or transient reverse flow reactor operation, e.g. to process lean waste gases or to perform efficiently slightly exothermic equilibrium limited reactions. This work explains the periodic operation of a multi-bed reactor network using both a simplified model assuming a true counter current of the phases involved and a more detailed dynamic model. An appropriate expression for relating the switching times and solid phase velocities is applied. The shapes of the thermal waves are studied in a range of relevant switching times. Results of a stability analysis considering both models reveal hysteresis for ignition and extinction of the reactor network. The accompanying regions of multiplicity provide insight in the potential of performing in such reactor networks exothermal reactions for certain ranges of the adiabatic temperature rise. (C) 2009 Elsevier Ltd. All rights reserved.