In this these we analyse the mathematical models of the interaction between predator and prey that have been expressed as a system of nonlinear ordinary differential equations. We have analysed the steady-state operations of a simple bioreactor, with or without death coefficients of predator and prey. The interaction between predator and prey is assumed to be governed by the well-known Monod growth kinetics. The steady-state solutions of the models are found and their stability determined as a function of the residence time. The performance of the bioreactor at large residence time is obtained.