The steady state of a non-isothermal packed-bed reactor (PER) is convectively unstable in the sense that upstream perturbations are amplified in the course of their downstream propagation before they are washed out by the flow. The differential-flow instability (DIFI) that underlies this dynamics arises from the different rates of transport of heat and matter in the PER and from the autocatalytic nature of the reaction heat. In the PER with recycle, the DIFI has an absolute character and it results in self-sustained, periodic wave activity. The DIFI-concept provides a theoretical framework for interpreting and analysing several types of wave phenomena in PBRs.