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Current approaches to model-based conformance testing of real-time systems are mostly based either on finite state machines/transition systems or on timed automata. However, most real-time systems manipulate data while being subject to time constraints. The usual solution consists in enumerating data values (in finite domains) while treating time symbolically, thus leading to the classical state explosion problem. This paper proposes a new model of real-time systems as an extension of both symbolic transition systems and timed automata, in order to handle both data and time requirements symbolically. We then adapt the tioco conformance testing theory to deal with this model and describe a test case generation process based on a combination of symbolic execution and constraint solving for the data part and symbolic analysis for timed aspects.