In a typical plant, downstream separators are coupled to upstream reactors through recycle streams. The bifurcation behavior of the coupled system is different from that of the individual units. The bifurcation diagram depicts the dependence of the steady state on an operating parameter. In this work, we analyze the behavior of three different coupled reactor-separator systems. Each system is characterized by a different separator. The three different separator units investigated are a flash unit, a nanofiltration unit, and an ultrafiltration unit. The reactor is modeled as a CSTR sustaining a cubic autocatalytic reaction. The stand-alone reactor can have a maximum of three solutions. The coupled system is investigated for the situation when the fresh feed is flow controlled and the reactor level is maintained constant using the reactor effluent flow stream. It is shown that the coupled reactor-flash system has a maximum of two steady solutions, while the two coupled reactor-membrane separation systems have a maximum of three solutions. Each coupled process is analyzed for two situations: (i) a binary system and (ii) ternary system. The physical cause for the difference in these behaviors is analyzed.