This paper describes a scheduling algorithm for a set of tasks that guarantees the time within which a task, once started, will complete. A task is started upon receipt of an external signal or the completion of other tasks. Each task has a rxed set of requirements in processor time, resources, and device operations needed for completion of its various segments. A worst case analysis of task performance is carried out. An algorithm is developed for determining the response times that can be guaranteed for a set of tasks. Operating system overhead is also accounted for.