A continuous flow bioreactor is a well-stirred vessel containing microorganisms (X) through which a substrate (S) flows at a continuous rate. The microorganisms grow through the consumption of the substrate, producing more microorganisms and products. The products will typically contain carbon dioxide, nitrogen, water and other species, including biological compounds, specific to the process under consideration. The nature of these products is unimportant in this study. Unused substrate, microorganisms, and products flow out of the reactor. The use of a continuous flow bioreactor to treat sewage or industrial wastewaters is known as the activated sludge process. One drawback associated with the activated sludge process is the production of 'sludge'. Traditional methods for disposing of excess sludge, which include incineration, the use of landfill sites and dumping at sea, are becoming increasingly regulated in many countries due to environmental concerns about the presence of potentially toxic elements in the sewage sludge. Furthermore, a combination of the limited amount of land available for landfill, particularly in urban areas, with stringent legislation has seen the economic costs of using landfill sites to increase sharply. It should be noted that incineration does not eliminate the need for landfill sites as a product of incineration is an ash containing high heavy materials content and general toxicity. Thus there is a pressing need, and growing interest, in methods that reduce the volume and mass of excess sludge produced as part of biological wastewater treatment processes. A promising method to reduce excess sludge production is to increase the biodegradability of the sludge by disintegrating it within the reactor. This approach works primarily by causing the disintegration of bacterial cell walls. Among the many techniques that have been reported for application to the activated sludge process, chemical treatments and ozone treatments have been the most widely adopted commercially [Oh et al (2007)]. In processes involving ozonation a part of the sludge is removed from the reactor and treated with ozone in a sludge disintegrator. This ozonation stage converts the live sludge into a mixture of soluble substrate and particulates. The liquidized sludge is then returned to the bioreactor as a feed solution where the soluble substrate is biodegraded by live sludge. These techniques have shown to lead to much lower levels of MLSS (mixed liquor suspended solids). A simple model is considered for a reactor cascade in which each reactor may be connected to both a settling unit and a sludge disintegration unit (SDU). The sludge disintegration unit is not modelled per se. Instead sludge disintegration terms are added to a conventional activated sludge model. These terms assume that the disintegrator unit destroys the biochemical activity of the sludge, converting a fraction, α, directly into usable substrate and the remainder, (1 - α), into organic particulates. We obtain a qualitative understanding of the performance of the process by finding the steady-state solutions of the model and determining their stability. For a specified mixed liquor suspended solids (MLSS) content the values of the dimensionless residence time and the sludge disintegration factor are determined that ensure zero excess sludge production. We show that if the sludge disintegration factor is sufficiently high then the MLSS content is guaranteed to be below the target value provided that the residence time is higher than the washout value.