This paper deals with the existence and stability of multiple equilibrium profiles in tubular bioreactors. We prove here that a tubular biological reactor can posses one or several equilibrium profiles according to the dispersion and convection terms as long as the kinetic function belongs to a general class of non-monotonic functions. Such systems allow the characterization of the hydrodynamic behavior of most real systems in classifying them between completely mixed systems and perfect Plug Flow systems. The stability analysis of equilibrium profiles is also carried out and it is shown that they are alternatively stable, unstable, stable, etc.