A mathematical model involving a syntrophic relationship between two
populations of bacteria in a continuous culture is proposed. A detailed
qualitative analysis is carried out. The local and global stability analysis of
the equilibria are performed. We demonstrate, under general assumptions of
monotonicity, relevant from an applied point of view, the asymptotic stability
of the positive equilibrium point which corresponds to the coexistence of the
two bacteria. A syntrophic relationship in the anaerobic digestion process is
proposed as a real candidate for this model
