The periodic behaviour of a large class of unstructured kinetic models for continuous bioreactors is analyzed using elementary concepts of singularity theory and continuation techniques. The class consists of models for which the utilization rate of the limiting substrate is linearly related to the rates of cell growth and product formation. The model kinetics are allowed, on the other hand, to depend on substrate, biomass and product. The stability analysis allows the derivation of general analytical conditions for the occurrence of periodic behaviour in these models. It is shown that for a number of important cases, the occurrence of oscillatory behaviour is conditioned mainly by the kinetics of product formation. The singularity theory also allows the construction of a useful picture in the multidimensional parameter space delineating the different behaviour these models can predict including bistability and stable oscillatory behaviour.