Fed-batch reactors, with cyclical feeds and extractions, are used in fermentations. The behaviour of this type of reactor under quasi-steady state is discussed. With fermentations, the washout conditions are calculated for cases of homogeneous fermentation and for heterogeneous fermentation. In the case of heterogeneous fermentation (fermentation of particulate substrate), the residence time distribution of the solids has been taken into account. Fed-batch reactors can also be used as differential reactors. The performance equations deduced are used for correlating the experimental data obtained in the anaerobic digestion of sewage sludge.