In this work, the stability structure of process flow sheets described by systems of differential and algebraic equations (DAE’s) is analyzed. This general framework allows the study of some of the dynamics and stability problems that arise in polymerization processes. A new numerical driver (ISAAC) which is a part of the dynamic flow-sheeting package POLYRED (polymerization reactor design) is used to perform continuation studies and steady-state stability analysis. The Himont liquid pool loop reactor and the Unipol gas-phase fluidized bed reactor are presented as examples of real systems which can become unstable because of the nature of the now-sheet topology and operating conditions selected.