In this thesis I analyze a mathematical model for uncompetitive product inhibition in a continuous flow bioreactor. The reaction is assumed to be governed by Monod growth rate kinetics subject to noncompetitive product inhibition. This model is represented by a system of three non-linear ordinary differential equations. The dimensional form is scaled by using dimensionless variables to get the dimensionless form. The region for the mathematical model is shown to be positively invariant. Moreover, it is shown what is the behaviour of the model for large values of the dimensionless death rate. The steady-state solutions of the model are found and their stability determined as a function of the residence time, which is the main experimental control parameter. The performance of the bioreactor at large residence time is obtained. The steady-state diagrams are plotted for the physically meaningful solutions and the asymptotic solution for large residence time.