Food processing wastewaters and slurries typically contain high concentrations of biodegradable organic matter. Before the wastewater can be discharged, the pollutant concentration must be reduced. One way to achieve this is by using a biological species (biomass) that consumes the organic matter (substrate). We investigate an unstructured kinetic model for a bioreactor with a variable yield coefficient, taking into account the death rate of the microorganisms. The growth rate is given by a Contois expression, which is often used to model the growth of biomass in wastewaters containing biodegradable organic materials. The analysis shows that the system has natural oscillations for some ranges of the parameters. We also investigate the effects of the death rate parameter on the region of periodic behaviour. © Austral. Mathematical Soc. 2012.