In this work, we study a model describing a syntrophic relationship of two microbial species with two input substrates, including both decay terms and inhibition of the first species by an excess of the second substrate. This model can be seen as a reduced and simplified version of the anaerobic digestion process. We discuss the existence and stability of all equilibria and we give necessary and sufficient conditions on the control parameters of the system (the dilution rate D and the input concentrations of the two substrates s in 0 and s in 1). By means of operating diagrams, we describe the asymptotic behavior of the model with respect to the control parameters and we illustrate the effect of the second input substrate.