Abstract
The usual models of the chemostat assume that the competition is purely exploitative, the competition is only through the consumption of the nutrient. However, it is known that microorganisms can produce toxins against its competitors. The basic experiments are due to Chao and Levin. In this work, we consider a model of competition in the chemostat of two competitors for a single nutrient where one of the competitors can produce a toxin against its opponent at some cost to its reproductive abilities. We give a complete characterization of the outcome of this competition in terms of the relevant parameters in hyperbolic cases. In three of four cases, the asymptotic results are global.