Abstract: Both effective resource utilization and meeting the deadlines of high-criticality tasks are objectives of mixed-criticality systems. Currently, it is considered the moment that any of high-criticality tasks execute for their low-critical worst case execution time without completing the system switch from low to high-criticality mode immediately. However, in real embedded applications, the increasing criticality is event-triggered which includes outer circumstance changing, control switching, and so on. That is why the time of raising criticality level can be occurred before, during, or after a task implementation. In this paper we center on that the time of event-triggered increasing criticality is how to influent the scheduling of high-criticality and fixed priority periodic tasks, which is based on the response time analysis. A sufficient condition of scheduling high criticality tasks is derived. Then we discuss when and how to exchange priorities between two high-critical tasks in order to meet their deadlines at the same time, and propose an algorithm of exchanging priorities. Evaluations illustrate the benefits of the schedulable condition and the priority exchanging algorithm.