Mathematical models of great complexity are being developed to help in understanding the behavior of ecosystems, but succinct conclusions for large models are difficult to obtain. In this report, criteria are introduced that guarantee that a given food-web model has no more than one equilibrium point. These criteria consist of biologically reasonable constraints on the behavior of the growth rates of the species as functions of population density plus the restriction of the food web to loops of lengths 1 and 2. While this last condition probably does not hold for most real food webs, the theorem may be robust enough to apply over a large range of cases. Our analysis also suggests that increasing complexity in food-web models might be accompanied by a greater number of equilibrium points. Therefore, the chance of a system having at least one stable equilibrium point could increase as complexity increases, a conclusion of interest in the current debate over the relationship between stability and complexity.