A detailed study of the dynamics of a packed-bed reactor containing immobilized enzyme particles is presented. The analysis consists of (i) transient state behavior; (ii) models for interphase and interfacial mass transfer between fluid and solid phases and intraphase mass transfer for the solid phase; (iii) detailed reaction rate model for the Bodenstein intermediates; (iv) mass balances for substrates, Bodenstein intermediates, unoccupied enzyme active sites, and products; and (v) models for enzyme denaturation and elution. The general reactor model consists of a set of nonlinear, coupled, partial differential equations. Numerical solutions of the system equations were obtained, using the discrete-space, continuous-time method of lines and realistic parameter values. A generalized map of the range of validity of the Steady-State Hypothesis was established under conditions where multiple mass transfer gradients were present within the reactor. A detailed analysis of the computational errors was performed. It was conclusively shown that the computer simulation solutions obtained in the analyses were not disguised to any significant degree as a result of employing finite difference approximations to the spatial derivatives. It was shown that the level of “error” involved in invoking the Steady-State Hypothesis depends on the relative magnitude of the kinetic parameters and also on the level of “disturbance” at the reactor inlet (i.e. per cent change in substrate inlet concentration). The “error”, however, did appear to be strikingly insensitive to the magnitude of the resistances to mass transfer, as characterized by the Modified Sherwood Number. It was concluded that, given any complete set of kinetic parameters, a transient, heterogeneous, isothermal reactor model based on the Steady-State Hypothesis may be used for predicting time-varying concentration profiles for minor (i.e., less than 5 per cent change in substrate inlet concentration) “disturbances” at the reactor inlet. The corresponding “errors” would be at an acceptable level (i.e., less than 2 per cent in the concentration and less than 10 per cent in the time lag) under these conditions. Further, various mechanisms for enzyme denaturation and elution were incorporated in the general reactor model. Numerical solutions of the resulting system of partial differential equations were obtained, using hypothetical parameter values. Through extensive simulation research, it was shown that the loss in activity of immobilized enzyme reactors cannot be uniquely ascribed to any one particular set of mechanistic deactivation modes.