A dual-rate system with fast input and very slow output is very common in the chemical process industry. To identify its original fast single-rate model based on the output error method, a two-stage method combining techniques for dealing with initialization and local minimum problems is proposed in this paper. In its first stage, a finite impulse response (FIR) model is developed directly from the original dual-rate sampled data using the combined least-squares criterion and Newton-Raphson (N-R) method. In the second stage, a single-and-fast-rate output error model is developed on the basis of the original fast input signal and the derived slow rate model output. Besides the simulation examples, the method is also applied to develop a composition observer for an industrial distillation column.