In this work, the dynamic behavior of two chemical reactors (Fixed Bed Catalytic Reactor and the Three-Phase Reactor), in which different reactions of great industrial interest take place, is presented. Rigorous and reduced models were developed and their capabilities to adequately predict the dynamic behavior of these reactors were compared, indicating which model is more suitable for a specific application (design, optimization and control). Different approaches [Classic, Hermite, Finlayson, Pirkle, Dixion, Generic and Orthogonal collocation (one point)] were used to obtain the reduced models. With these techniques, a mathematical order reduction was carried out, which eliminates the spatial co-ordinate (of the catalyst particle or of the reactor) and promotes radially lumped-differential formulations. The proposed rigorous models were able to predict the main characteristics of the dynamic behavior of the fixed bed catalytic reactor as well as of the three-phase reactor, including the inverse response phenomena and the hot spot present in the former. This knowledge is essential to design and control these reactors. The computational time demanded for the solution of the rigorous models is high in comparison to the reduced ones, which restricts the use of the rigorous models to cases where time is not a limiting factor. Otherwise, when on-line applications are required, the reduced models are more adequate. The models based on reduction techniques overcame computational burden with a faster and easier numerical solution, as well as other difficulties found in rigorous heterogeneous models, especially related to the large number of parameters and sophisticated numerical procedures required by the solution. © 2008 Berkeley Electronic Press. 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