A mathematical model of an aerobic biofilm reactor is presented to investigate the bifurcational patterns and the dynamical behavior of the reactor as a function of different key operating parameters. Suspended cells and biofilm are assumed to grow according to double limiting kinetics with phenol inhibition (carbon source) and oxygen limitation. The model presented by Russo et al. is extended to embody key features of the phenomenology of the granular-supported biofilm: biofilm growth and detachment, gasliquid oxygen transport, phenol, and oxygen uptake by both suspended and immobilized cells, and substrate diffusion into the biofilm. Steady-state conditions and stability, and local dynamic behavior have been characterized. The multiplicity of steady states and their stability depend on key operating parameter values (dilution rate, gasliquid mass transfer coefficient, biofilm detachment rate, and inlet substrate concentration). Small changes in the operating conditions may be coupled with a drastic change of the steady-state scenario with transcritical and saddle-node bifurcations. The relevance of concentration profiles establishing within the biofilm is also addressed. When the oxygen level in the liquid phase is <10% of the saturation level, the biofilm undergoes oxygen starvation and the active biofilm fraction becomes independent of the dilution rate. (C) 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011