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Hybrid input/output automata provide a language for the description and analysis of hybrid systems. In this paper, we develop a notion of approximate simulation relation for metric hybrid input/output automata, which is an extension classic simulation relation in hybrid input/output automata, and investigate some interesting results. In addition, we discuss a particular kind of approximation simulation relation, i.e. approximate refinement. Moreover, we show how to adopt approximate synchronization methods to guarantee substitutive under the condition of approximate simulation.