The stability and dynamic behavior of two types of continuous stirred bed reactors (CSBR) has been analyzed. Both the vertical CSBR of BASF and the horizontal CSBR of Amoco are examined. In each case, it is seen that multiple steady states and limit cycle oscillations are possible when the temperature controller is not in service. For the practical range of operating conditions, limit cycle oscillations with temperature excursions above the polymer melting point are the principle danger. For the Amoco reactor there are many possible reactor models which satisfy the observed production rate and residence time distribution. The particular dynamic behavior depends strongly on model choice.