We consider the problem of scheduling hard real-time tasks subjected to preemption delays on a uniprocessor. Most existing works focus on either reducing these delays or improving the system predictability by bounding them. But not much has been studied about the matter of taking scheduling decisions while considering preemption delays. We first consider the online scheduling problem and show that EDF is not optimal any more as soon as preemption delays are not neglected. Moreover, we prove that there exists no optimal online algorithm for the problem of scheduling a set of jobs with preemption delays. Then, we consider the offline scheduling problem and propose a mathematical model to compute an optimal solution to our problem.Best Paper A...