This article concerns the problem of nonlinear state-observer design. It presents a reduced-order nonlinear observer design approach, which allows adjustment of the rate of the decay of observer error and is easy to use. Furthermore, in many chemical engineering cases, it is straightforward to prove analytically that the observer-error dynamics are globally asymptotically stable. Several classes of reactors (classical chemical reactors, free-radical polymerization reactors, and bio-reactors) are considered to illustrate the application of the observer design approach. The global asymptotic stability of the observer-error dynamics is proved for each class of the processes. For many of these processes, this study presents the first observer with an analytically proven global convergence.