Steady state behavior of a continuous stirred tank reactor is analyzed for styrene polymerization with bifunctional free radical initiators. Compared with polymerization by monofunctional initiators, the bifunctional initiator system produces polymers of significantly high molecular weight at high monomer conversion. This is due to the presence of multiple labile peroxide groups having distinctively different thermal decomposition characteristics. The steady state reactor model analysis indicates that five unique regions of steady state behavior are present in a parameter space with reactor residence time as a bifurcation parameter. It is also shown that a broad range of polymer properties can be obtained by judiciously choosing the reactor operating conditions with the bifunctional initiator.