Material and temp. instabilities in autothermal reactors, e.g. catalyst temp. instabilities and steep radial and axial temp. profiles, and difficulty in isolation of intermediate products, are resolved by periodic operation of the reactor. Using the oxidn. of propylene over Pt gauze as an example, it was shown that operation at high frequency within the temp.-conversion hysteresis allows the reactor to operate in a pseudostationary mode at one of the stable operating points. Increasing the mass capacity or the periodic frequency lowers the concn. amplitude. The cycle amplitudes are mainly detd. by the heat capacity of the system.