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The aim of this article is to show, how a multitasking application running under real-time operating system compliant with OSEK/VDX standard can be modeled by timed automata. The application under consideration consists of several tasks, it includes resource sharing and synchronization by events. For such system, we use model checking theory based on timed automata and we verify time and logical properties of proposed model by existing model checking tools. Since a complexity of the model-checking verification exponentially grows with the number of clocks used in a model, the proposed model uses only one clock for measuring execution time of all modeled tasks.