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 (gamma) 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 gamma is a scaled inhibition constant (Kp) that depends upon the substrate and product yield factors and the Monod constant.