This paper concerns the problem of state estimation in nonlinear deterministic processes. For moderately nonlinear deterministic processes, the inadequacy of full-order Luenberger observer and extended Luenberger observer with constant gain is shown analytically and through numerical simulation of a chemical reactor. The results indicate that the convergence of an extended Luenberger observer with constant gain may be poorer than that of a simple linear Luenberger observer. A nonlinear observer design method with varying gain is applied to a classical exothermic stirred-tank reactor with multiple steady states. Under significant observer-initialization errors and several observer gains, the global asymptotic convergence of the nonlinear observer is demonstrated through numerical simulations. In the presence of the multiple steady states, the nonlinear observer converges to the same steady-state operating point at which the reactor operates, irrespective of the observer initial conditions.