OpenMP is increasingly being considered as a convenient parallel programming model to cope with the performance requirements of critical real-time systems. Recent works demonstrate that OpenMP enables to derive guarantees on the functional and timing behavior of the system, a fundamental requirement of such systems. These works, however, focus only on the exploitation of fine grain parallelism and do not take into account the peculiarities of critical real-time systems, commonly composed of a set of concurrent functionalities. OpenMP allows exploiting the parallelism exposed within real-time tasks and among them. This paper analyzes the challenges of combining the concurrency model of real-time tasks with the parallel model of OpenMP. We demonstrate that OpenMP is suitable to develop advanced critical real-time systems by virtue of few changes on the specification, which allow the scheduling behavior desired (regarding execution priorities, preemption, migration and allocation strategies) in such systems.