Evaluation of the energy efficiency of a fixed-bed reactor in cyclic operation, subject to alternate swings of an exothermic and an endothermic reaction, is the basis of this study. During an exothermic semi-cycle an exothermic reaction takes place to heat the bed while during an endothermic semi-cycle that follows an endothermic reaction takes place in the bed, with reactants fed into the bed from the opposite direction. A fixed-bed operated periodically in the above-described mode is asymmetric as the dynamic nature of the bed changes during each cycle. It is shown that to operate such an asymmetric fixed-bed reactor in a periodic steady state, two conditions need to be satisfied - the energy liberated during the exothermic semi-cycle should be equal to or greater than the energy consumed during the endothermic semi-cycle, and the product of the front velocity and semi-cycle period for the endothermic semi-cycle must be equal to or greater than that for the exothermic semi-cycle. The energy efficiency and conversions for both reactions increase with increasing bed length and decreasing semi-cycle periods for a fixed ratio of the exothermic and endothermic semi-cycle periods. The effect on operability and energy efficiency of the heats of reactions, inlet mass fluxes, front velocities during both semi-cycles, and of the ratio as well as the magnitude of individual semi-cycle periods is discussed.