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In this paper, we present a new compositional verification methodology for efficiently verifying high-assurance properties such as reachability and deadlock freedom of real-time systems. In this methodology, each component of real-time systems is initially specified as a timed automaton and it communicates with other components via synchronous and/or asynchronous communication channels. Then, each component is analyzed by a generation of its state-space graph which is formalized as a new state-space representation model called Multiset Labeled Transition Systems (MLTSs). Afterward, the state spaces of the components are hierarchically composed and simplified through a composition algorithm and a set of condensation rules, respectively, to get a condensed state space of the system. The simplified state spaces preserve equivalence with respect to deadlock and reachable states. Such equivalence is assured by our reduction theories called IOT-failure equivalence and IOT-state equivalence. To show the performance of our methodology, we developed a verification tool RT-IOTA and carried out experiments on some benchmarks such as CSMA/CD protocol, a rail-road crossing, an alternating bit-protocol, etc. Specifically, we look at the time taken to generate the statespace, the size of the state space, and the amount of reduction achieved by our condensation rules. The results demonstrate the strength of our new technique in dealing with the state-explosion problem.