In previous work ( Freedman and Wolkowicz, 1986; Bull. math. Biol. 48, 493–508) it was shown that in a predator-prey system where the prey population exhibits group defence, it is possible that enrichment of the environment could lead to extinction of the predator population. In this paper a third population is introduced and criteria are derived under which persistence of all populations will occur. In particular, criteria for a superpredator and for a competitor to stabilize the system in the sense of persistence are analyzed.