The zero dynamics of simple continuous and fed-batch biore-actors is investigated in this paper for different input and output selections. A function λ generating the necessary coordinates transformation has been determined analytically for each case solving a simple PDE, and the resulting coordinates transformations have found to be invertible on the physically meaningful operating region. It is shown that that the investigated continuous and fed-batch bioreactors are globally minimum phase systems with the examined reaction rate function if the manipulable input is the inlet feed flow rate and the output is the substrate concentration. It is also shown that the zero dynamics may have multiple (locally stable and unstable) equilibria if the input is the inlet feed flow rate and the output is the biomass concentration.