Assessing the consequences of exceptional events, such as failures and sudden changes in product demand or raw-material prices, is of great importance to the operation of chemical processes. Such an exceptional event and the resulting behavior of the process are called a scenario in this article. Problem formulations for their rigorous incorporation into the optimization of dynamic systems are presented. They allow the determination of operational strategies that are economically optimal and that keep the plant within a chosen regime in the state space, even for a number of possible scenarios. The formulations are based on a unifying model framework containing both continuous and discrete dynamics. For a restricted class of problems a method for the numerical solution of the resulting scenario-integrated dynamic optimization problems is introduced. The applicability of this technique is demonstrated with two examples of different complexity.