Abstract: In this paper, we point out the relations between event-order and several important properties of Discrete Event Dynamic Systems. We obtain a series of results on robustness of event-order for the maximum algebra DEDS model. A Kharitonov-like finite check criterion for robustness of event-order is given for the case in which the event occurrences are affine linear function of perturbed parameters. Vertex check is shown not sufficient to determine the robustness of event-order under more general circumstances by a counter-example. A sufficient condition for DEDS to preserve event-order under parameter perturbations is then given for the polynomial case.