A deep investigation has been carried out about the behaviour of a reverse-flow combustor for the treatment of low-VOC concentration waste gases, in the presence of periodical variations in the feed characteristics. Two kinds of variations have been taken into consideration: in the inlet concentration and in the flow rate. In both cases, the variations cause relevant fluctuations in the maximum temperature of the bed and in conversion. These fluctuations, especially for long feeding cycle periods, can endanger the correct operation of the reactor. In addition, for particular ratios between the feeding cycle period and the flow-reversal cycle period, the interaction between the two cycles may cause serious problems of instability, represented by large low-frequency fluctuations of the maximum temperature in the case of variations in the inlet concentration, and by a dangerous flow asymmetry in the case of variations in the flow rate. The criteria to avoid these problems are presented.