A general dynamic model of monolith catalytic reactors is developed to elucidate the intricacy of the physicochemical phenomena that occur in it. The dynamic model includes microkinetic reactions on a washcoat catalyst, which is incorporated in a heat- and mass-transfer submodels based on the quasi-2D analysis of both gasand solid-phases. To support the derived general dynamic model, a dimethyl ether (DME) catalytic reactor that uses Pt/ZSM-5 catalyst is developed and simulated. The model prediction is validated using experimental data under nearly stoichiometric, lean, and rich conditions. The results demonstrate the catalytic conversion and selectivity of DME, distribution of the wall temperature, distribution of the species concentrations in steady-state, and transient response of the catalytic reaction. We found that the time response of the lowest inlet-gas temperature can be yielded similar to 6 min, but the DME conversion is limited under the low-temperature condition.