The biodegradation of pollutants in continuous operation when the microbial population exhibits wall attachment is studied. The proposed model for wall attachment assumes two morphological forms of the microbial cell connected by metamorphosis reactions with first order exchange kinetics. An analysis of the stability of the bioreactor, carried out using elementary principles of the singularity theory and continuation techniques, allows for classification in the multidimensional parameter space of the various stability behaviors exhibited by the reactor model, for both substrate-inhibited and Monod kinetics, The analysis also shows the enhanced stability behavior of the bioreactor due to wall attachment. (C) 2000 John Wiley & Sons, Inc.