A method multirate nonlinear state observer design, which can use directly a non-linear process model in the observe design without any linear approximation, is presented. The multirate nonlinear state observer is easy to design and implement, and is computationally efficient. Furthermore, for a number of processes, it is possible to prove the global convergence of the multirate state observer analytically. The design, implementation and performance of the state observer design method are shown by a polymerization reactor in which free-radical solution polymerization of styrene takes place. The initiator concentration and three leading moments of the molecular weight distribution (MWD) of the polymer product are estimated continuously from: (i) frequent measurements of the reactor temperature, jacket temperature and reacting-mixture density; (ii) infrequent and delayed measurements of the leading moments of the MWD. Each infrequent measurement has a sampling period and a measurement delay of 0.5 or 1 h. In the presence of model-plant mismatch and measurement noise, the convergence of the multirate state observer is shown by numerical simulations.