This paper presents a dynamic model for a fixed or liquid fluid bed immobilized-enzyme bioreactor, together with a novel method for the solution of the coupled partial differential equations in the real-time domain. Both the tanks-in-series and the dispersion models are used to describe the non-ideal axial mixing in the reactor. The solution, in its final form, comes in both cases as a system of simultaneous ordinary differential equations that can be readily solved using commercially available software packages. Based on this solution, a complete parametric analysis was performed. The analysis revealed the importance of intraparticle and external mass transfer resistances, intraparticle chemical reaction and axial dispersion on the transient behaviour of the reactor. Most important, the analysis revealed ways for parameter estimation and system identification via simple dynamic experiments. The design and optimization implications are demonstrated by using the derived solution to simulate the performance of an immobilized-urease fluidized-bed bioreactor with a recycle loop. Such a configuration is characterized by a time-varying feed concentration and can be used, as part of an extracorporeal artificial kidney device, for the treatment of uremic patients.