Abstract : Non-preemptive real-time scheduling and the corresponding schedulability analyses have received considerable less attention in the research community, compared to preemptive real-time scheduling. However, non-preemptive scheduling is widely used in industry, especially in the case of hard real-time systems where missing deadlines leads to catastrophic situations and where resources must not be wasted. In many industries such as avionics tasks may have strict periods, i.e. the start times of their executions must be separated by a fixed period. Indeed, this strict periodicity is generally required by sensors and actuators which may have accurate periods. In this paper we consider separately the case where tasks have harmonic periods and the case where tasks have non-harmonic periods. Thus, the general case becomes a combination of both cases. In the harmonic case we give schedulability conditions to verify that a set of tasks is schedulable. In the non-harmonic case, in order to prove that a set of tasks is schedulable we propose local schedulability conditions that we apply iteratively to each task of the set in order to verify that this current task, added to a sub-set of tasks already scheduled, leads to a schedulable set of tasks.