This paper deals with the analysis of the equilibria and their stability of the so-called AMOCO model developed by Bernard and ali (2001) to describe the dynamical behavior of an anareobic fixed-bed wastewater treatment process. Depending on the model parameters, the steady states are analytically characterized and their stability is analyzed. Following this study, it is shown that the overloading tolerance (denoted herein OT), a parameter proposed in Hess and Bernard (2007) to on-line monitoring anaerobic processes, may be not adapted under certain operating conditions and even lead to bad operating decisions.