Fixed-bed reactors with periodic flow reversal are used to carry out reactions with low exothermicity in an autothermal way. Contrary to conventional autothermal reactors, the preheating of the feed gas is accomplished by regenerative heat exchange between the gas and fixed bed. The feedback of heat and direct coupling of heat exchange and chemical reaction give rise to an unusual reactor behavior. This behavior can be understood through consideration of the limiting cases of very long and very short cycle periods. Both cases can be calculated easily with the methods presented. Especially for the case of rapid flow reversal, simple equations can be derived that allow for a good physical understanding of the process and for a preliminary reactor design. In this case, it is also possible to compute the unstable solution, which is a lower bound of the temperature profile necessary for reactor startup.