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When a large-scale distributed interactive simulation system is running on WAN, the sites usually disperse over a wide area in geography, which results in the simulation clock of each site is hardly to be accurately synchronized with that of other sites. The asynchronous clocks and large transmission latency on WAN bring on a problem for the large-scale simulations to preserve the real-time causal order delivery of received events at each site. In this article, we analyze the indirect way to compare the values of asynchronous simulation clocks at first, and then propose a novel scheme which can select the reconstructible causal control information for each message so as to ensure the causal ordering of events in real time. Experiments demonstrate that the scheme can weaken the effect of network latency, reduce the overhead of the transmission amount of control information and improve the causal order consistency in asynchronous distributed simulations.