A mathematical model for a two-phase fluidised bed bioreactor with liquid recirculation and an external aerator was proposed. A stationary nonlinear analysis of such a bioreactor for an aerobic process with double-substrate kinetics was carried out. The influences of a volumetric fraction of solid carriers in the liquid phase, the rate of active biomass transfer from the biofilm to the liquid, the concentration of carbonaceous substrate, the mean residence time of the liquid and the efficiency of the external aerator on the steady state characteristics of the bioreactor were described. A method for determination of the minimal recirculation ratio related to oxygen demand and fluidised bed conditions was presented. On the basis of the obtained results, it is possible to choose reasonable operating conditions of such plants and to determine constraints, while considering acceptable concentrations of a toxic substrate being degraded.