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In this paper, we propose an approach for the development of real time systems and applications with a formal support based on rewrite logic. The design pattern based development process permits to represent the real time design patterns according to the new profile “DPP-RTSA” and provide, so, a manner to correctly execution of the instantiation and the composition of patterns. The obtained design from the application of the proposed process is translated into formal specification in rewriting logic (RT-Maude). The execution of this RT-Maude specification serve to perform the verification of the modelled system proprieties.