The nonlinear behavior of a coupled reactor-separator network was analyzed using singularity and bifurcation theory. The reactor was modeled as a CSTR, which sustains an exothermic first-order reaction. Two different modes of operation were considered, which could be achieved by a suitable control strategy. The behavior of the reactor separator network crucially depended on the mode of operation. Interesting patterns of behavior were observed for the first mode of operation with externally fixed feed rate. This type of behavior was completely different from the classical problem, i.e., a stand alone CSTR with a first-order exothermic reaction. For the second mode of operation, the recycle rate was fixed. The nonlinear behavior of the reactor separator network with fixed recycle rate was quantitatively similar to the corresponding stand alone reactor. Particularly, at least one feasible and stable steady-state solution existed for all physically reasonable parameter values. Hence, this second control structure was preferable over the first.