The steady-state production of a product produced through the growth of microorganisms in a continuous flow bioreactor is presented. A generalised reactor model is used in which both the classic well-stirred bioreactor and the idealised membrane bioreactor are considered as special cases. The reaction is assumed to be governed by Monod growth kinetics subject to non-competitive product inhibition. Inhibition is modelled as a decaying exponential function of the product concentration. This reaction scheme is well documented in the literature, although a stability analysis of the governing equations has not previously been presented. The performance of a well-stirred bioreactor with microorganisms death is also not currently available in the literature. The steady-state solutions for the models have been obtained, and the stability has been determined as a function of the residence time. The key dimensionless parameter (γ) that controls the degree of non-competitive product inhibition is obtained by scaling of the equations, and its effect on the reactor performance is quantified in the limit when product inhibition is ‘small’. The parameter γ is a scaled inhibition constant (Kp) that depends upon the substrate and product yield factors and the Monod constant (). Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.