The stability characteristics of a bioreactor with cell recycle involving the competition between microbial cultures are investigated. The unstructured model, based on Andrew＇s inhibitory kinetics, involves the pure and simple competition between two microorganism for a single pollutant. The singularity theory used for this study allows an in-depth analysis of both the static and dynamic bifurcation mechanisms occurring in the system. The hysteresis with five solutions is the highest singularity the system can exhibit. With inhibitory kinetic expressions, the model can also predict self-sustained oscillations for a wide range of parameters. The analysis of clean feed conditions shows that the model cannot exhibit periodic behavior regardless of the growth kinetics model. Analytical criteria are also derived for the coexistence of the competing cultures and for the prevention of wash-out conditions. The stability characteristics for Monod kinetics, derived as a limiting case of the inhibitory kinetic expressions, are incorporated in the general framework offered by the singularity theory.