This paper concerns nonlinear state estimation in a continuous polymerization reactor where free-radical solution polymerization of methyl methacrylate takes place. Initiator and solvent concentrations and the leading moments of the molecular weight distribution of the polymer are estimated in three measurement cases. For one of the measurement cases, the global convergence of the nonlinear observer is proved. The convergence of the nonlinear observers is shown by numerical simulations, for different values of observer gains, for different observer initial conditions, and in the presence of a measurable disturbance. Furthermore, in each case, the implementation and performance of the nonlinear observer are compared with those of a deterministic extended Kalman filter.