The stationary state of a non-isothermal tubular packed-bed reactor with partial recycling of the product how or simply of the reaction heat, is shown to be absolutely unstable. This instability is closely related to the convective instability of a fixed-bed reactor without recycling [Yakhnin et al., 1994, Chern. Engng Sci. (in press)] which manifests itself as the ability of the system to amplify perturbations in the course of their spatial propagation. Recycling causes these amplified perturbations to be reinjected, thereby keeping the reactor from settling into its stationary state. This results in self-sustained periodic waves that circulate through the reactor.