On the basis of a general model the role of a predator is investigated in its coexistence with two competitive species in a chemostat, one of which is considered as prey. Results of nonnegativity and boundedness of solutions are stated. Further is shown the existence of a hierarchy of critical points and the transfer of global stability from one point to another with the change of parameters.
Three notions of persistence are introduced, namely persistence, weak and uniform persistence. The latter is practically the most desirable for population models. The uniform persistence of the model is proved on some conditions of differentiability and convexity. Finally, an example is considered. The predictive role of the model for laboratory experiments is discussed.