The multiplicity features of a continuous stirred tank reactor with vapor recycle have been studied for a dimerization reaction with second-order kinetics. Such reaction systems are common in the polymer industry. The aim of the analysis is to provide a simple design methodology that will ensure safe operation of the reactor. It is shown that solutions with and without vapor recycle exist. The bifurcation set for the system is calculated, and 11 different bifurcation diagrams arise. A linear relationship exists between the system parameter values, when these are normalized by their values at the ignition point. This leads to a simple method for defining a safe operating point for the system under a defined disturbance. (C) 2012 American Institute of Chemical Engineers AIChE J, 59: 553-559, 2013