Abstract : We consider the problem of fixed priority scheduling of non-preemptive strict periodic tasks in conjunction with sporadic preemptive tasks. There are few studies about the scheduling problem combining these two kinds of tasks. Moreover, only few results are available on scheduling non-preemptive strict periodic tasks since their performance analysis gives low success ratios, except in the case of harmonic tasks. Also, strict periodic tasks are of great importance since they are in charge for example of sensors/actuators or feedback control functions which are all critical in feedback control systems. Such tasks must have the highest priorities in order to guarantee a correct behavior of the control system. Preemptive sporadic tasks can be used for non critical functions and have lower priorities. We first investigate the scheduling problem of non-preemptive strict periodic tasks by recalling an existing schedulability condition. This results in defining the first release times of strict periodic tasks that preserves the strict periodicity constraints. We show that the schedule of strict periodic tasks can have transient and permanent phases. Then, assuming that some non-preemptive strict periodic tasks have been scheduled, we characterize the release times of the sporadic tasks that maximize their worst case response times. We prove that these release times can be restricted to the permanent phase. For preemptive sporadic tasks, we extend the classical worst case response time computation to take into account non-preemptive strict periodic tasks. Finally, we consider the particular case where some of the sporadic tasks are alternate tasks to primary strict periodic tasks for fault-tolerance.