The dynamics of azeotropic distillation columns are significantly more complicated than those of simple binary columns. For changes in the internal flows, we initially observe a response in overall separation with a time constant that is similar to the one observed in binary distillation. However, we also observe a slow time-constant response, which is due to changes in the relative amount of entrainer in the extractive section. The fact that the gains for these two effects have different signs causes overshoot and, depending on the operating point, may also cause inverse responses with significant time constants. None of these phenomena are observed in binary distillation. They can be modeled by a simple second-order model. We also examine the open-loop dynamics for configurations aimed at dual-composition control. Just as in binary distillation there is a "high gain direction" that is obtained for changes in the external flows. The dynamics of this direction are hardly affected by changes in the operating point. The "low gain direction" is obtained for changes in the internal flows, just as in binary distillation, and also for changes in the entrainer feed flow rate. The properties of this direction change significantly with the operating point. For some operating points we observe overshoot and for other multivariable right-half-plane transmission zeros not observed in binary distillation.