Reactive chromatography, i.e., coupling chemical reaction and selective sorption, allows us to drive the chemical reaction beyond equilibrium and to separate its products. Chromatographic reactors exhibit a complex dynamical behavior, whose analysis is the objective of this work. The synthesis of ethyl acetate and water from ethanol and acetic acid on a commercial polystyrene-divinylbenzene acidic resin is considered. The results of experiments run in a laboratory-scale chromatographic reactor are reported. Experimental data are in good agreement with the results obtained using a fully predictive equilibrium dispersive model. This exploits an accurate description of both the multicomponent sorption equilibria on the resin, based on the extended Flory-Huggins model, and the kinetics of the heterogeneously catalyzed chemical reaction. The chromatographic reactor exhibits a rather rich dynamical behavior, which is a consequence of the dual role, as a catalyst and as a selective sorbent, played by the resin. In particular, it is characterized by the development of composition fronts traveling along the fixed bed column at well-defined propagation velocities. By interpreting the obtained results in terms of these classical nonlinear chromatography concepts, a deep insight into the dynamical behavior of the chromatographic reactor can be achieved. These findings can be usefully summarized in a master plot which allows us to identify the different dynamic regimes in the operating parameter space.