Mathematical modeling of continuous multiple bioreactors is complicated by two factors. First, the chemical environments differ in different reactors, so biomass receives an environmental shock when it is transferred between reactors. Second, biomass occurs as discrete cells, which of course are and remain segregated from one another, so an element of biomass that enters a reactor does not mix with the biomass already present. This differs from the behavior of an element of liquid which enters a reactor in that such an element quickly mixes with the liquid already present. The biomass in a bioreactor receiving biomass from an external source is therefore heterogeneous with respect to the history of environmental conditions and composition. This article shows how to construct a mathematical model of multiple bioreactor apparatus that accounts for these complications. It also describes simpler models that do not account for both of them.