The effects of external film resistances on the deactivation of a single catalyst pellet are examined. Investigations on the isothermal fouling are first considered and are then extended to non-isothermal fouling for both endothermic and exothermic reactions. A pseudo-steady state for the reaction system is assumed with Langmuir Hinshelwood type of kinetics for the main reaction while for fouling, first order kinetics with respect to active sites and the fouling precursor concentration are adopted. Orthogonal collocation and a modified collocation—effective reaction zone method are employed to solve the proposed model.