Local steady state multiplicity may occur in a bed of cells immobilized within pellets or hollow fibres owing to coupling of diffusion resistance and a consumption rate. Local bistability, within a range of operating conditions in the bed, may lead to numerous solutions for the total conversion since t domains, may be placed at any position inside the reactor. The incorporation of longitudinal diffusion in the cell phase would cause such fronts to pro or reach a structurally stable position. Design criteria have been developed in the form of multiplicity domains for the local reaction-diffusion probl is analysed for diffusion resistance in the membrane as well as in the cell layer. The conditions which induce stationary fronts are analysed and up to inhibition is known to induce bistability in a chemostat (e.g. ammonia and nitrite oxidation by Nitrosomonas and Nitrobacter respectively). reactors for such processes. The results are illustrated by analysing the process of phenol degradation.