Models of anaerobic digestion are highly parameterised with many state variables. However, this complexity makes it intractable to identify the stability profile coupled to the the asymptotic behaviour of existing steady-states as a function of conventional chemostat operating parameters (substrate inflow concentration and dilution rate). Reduced models of the process have been shown to capture the underlying dynamics whilst enabling numerical and analytical studies of the ecological interactions and functions. Here, a three-tiered food-web model of anaerobic chlorophenol mineralisation is described that includes syntrophy, interspecific feedback competition, and product inhibition. Numerical analysis showed that the positive equilibria were always stable but suggested emergent behaviour was possible. A generalised form of the model was developed, whose results are valid for a large class of growth kinetics as long as they keep the signs of their derivatives. Analysis. of the existence and stability of the identified steady-states showed that, without a maintenance term, the stability of the system may be explored analytically. These findings permit a better understanding of the operating region of the bifurcation diagram where all organisms exist, and its dependence on the biological parameters of the model. When maintenance is included, global analysis of the positive equilibria is difficult, but the discovery of two important phenomena are shown; i) the washout steady-state is always stable, and ii) a switch in dominance between two organisms competing for hydrogen results in the system becoming unstable giving rise to interesting and previously unobserved dynamics. The results have importance beyond the studied cholorophenol system, specifically for any food-web in which an organism at a higher trophic level competes for a resource with a commensalistic organism at a lower trophic level.