Guaranteed response time is one of the important issues encountered in designing a real-time system. This problem has been studied with a new view by the AI community, which so far has proposed different paradigms. Anytime algorithms, Approximate processing, Design-to-time Scheduling and Progressive Reasoning are the most popular. All of them rely on a trade-off between run-time and quality of results. In the framework of the ESPRIT project n° 5146 and 7805 REAKT (REAl time Knowledge Tool), we have developed such a model called PROGRESS (PROGressive REasoning SyStem). This approach makes it possible to manage AI tasks with hard and soft deadlines, provided that multiple methods are available for the tasks the system has to solve. Thus, PROGRESS is closed to design-to-time real-time scheduling but it extends this approach for harder real-time constraints such that the system has the ability to react, meet hard and soft deadlines, stay alert to incoming events and reset task priorities according to changes in workload or resource availability. For this purpose, we have defined a new task model such that a task is not a priori defined at the time of its activation but step by step in the course of its execution. It is conceived as a process that gradually integrates changes and developments in the situation and in availability of resources. When unforeseen tasks have to be included in the schedule because of the occurrence of an unexpected event, the resulting overhead is dynamically accounted for an adaptation of on-going tasks. An on-going task can be reactively adapted as the subtasks composing the task are interruptible (as anytime algorithm can do). A task being constructed dynamically by composing design-to-time methods chosen in a library, we have developed a new deliberative scheduling algorithm which allocates to each component of the task the computation time which maximizes the output quality of the task.