The new reactor concept for highly endothermic reactions at elevated temperatures with possible rapid catalyst deactivation based on the indirect coupling of endothermic and exothermic reactions in reverse flow, developed for irreversible reactions in Part I, has been extended to reversible endothermic reactions for the sequential reactor configuration. In the sequential reactor configuration, the endothermic and exothermic reactants are fed discontinuously and sequentially to the same catalyst bed, which acts as an energy repository delivering energy during the endothermic reaction phase and storing energy during the consecutive exothermic reaction phase. The periodic flow reversals to incorporate recuperative heat exchange result in low temperatures at both reactor ends, while high temperatures prevail in the centre of the reactor. For reversible endothermic reactions, these low exit temperatures can shift the equilibrium back towards the reactants side, causing `back-conversion¿ at the reactor outlet. The extent of back-conversion is investigated for the propane dehydrogenation/methane combustion reaction system, considering a worst case scenario for the kinetics by assuming that the propylene hydrogenation reaction rate at low temperatures is only limited by mass transfer. It is shown for this reaction system that full equilibrium conversion of the endothermic reactants cannot be combined with recuperative heat exchange, if the reactor is filled entirely with active catalyst. Inactive sections installed at the reactor ends can reduce this back-conversion, but cannot completely prevent it. Furthermore, undesired high temperature peaks can be formed at the transition point between the inactive and active sections, exceeding the maximum allowable temperature (at least for the relatively fast combustion reactions). A new solution is introduced to achieve both full equilibrium conversion and recuperative heat exchange while simultaneously avoiding too high temperatures, even for the worst case scenario of very fast propylene hydrogenation and fuel combustion reaction rates. The proposed solution utilises the movement of the temperature fronts in the sequential reactor configuration and employs less active sections installed at either end of the active catalyst bed and completely inactive sections at the reactor ends, whereas propane combustion is used for energy supply. Finally, it is shown that the plateau temperature can be effectively controlled by simultaneous combustion of propane and methane during the exothermic reaction phase.