The mass balance equations for hollow fibre bioreactors have been solved for the zero-order limit of the Michaelis-Menten kinetics. As in the case of first-order reactions, the membrane and spongy matrix equations can be decoupled from the overall set of equations. For the case of the substrate remaining constant everywhere in the reactor a solution in terms of hypergeometric series is possible. For the substrate exhaustion case the extinction radius is a non-linear function of the system parameters and thus the equations have to be solved by numerical methods. © 1993.