Possible ways of coupling a solid-catalyzed endothermic reaction with an exothermic reaction in a bidirectionally fed fixed-bed reactor, operated in a periodic steady state, when the maximum allowable temperature is limited by either process, catalyst, or materials constraints, are discussed. Steam reforming of natural gas coupled with methane combustion is considered as an example. The catalyst bed is heated by the combustion reaction during the exothermic semicycle, while the endothermic reaction, with reactants fed from the opposite end, cools the bed during the endothermic semicycles. It is shown that two modes of periodic operation are possible. In the wrong-way process, reactants are fed at temperatures below the initial bed temperature, which results in maximum temperatures that can exceed the allowable limits. To suppress excessive temperature overshoots the fuel feed concentration must be very low, which leads, due to the creeping temperature hot zone, to only a small fraction of the heat produced during the exothermic semicycle being available for the endothermic reaction. Thermal efficiency and the reactor productivity are low. In the normal process, the inlet reactant temperature is above the ignition temperature, leading to a stationary spreadout temperature profile, high thermal efficiency, and high reactor productivity, as well as to controllable maximum temperature. Simulations for the wrong-way and normal processes are described as well as the possibilities of achieving very high thermal efficiencies in a process that integrates the reactor with heat recovery units.