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Multiparty interactive network applications such as teleconferencing, network gaming, and online trading are gaining popularity. In addition to end-to-end latency bounds, these applications require that the delay difference among multiple clients of the service is minimized for a good interactive experience. We propose a Latency EQualization (LEQ) service, which equalizes the perceived latency for all clients participating in an interactive network application. To effectively implement the proposed LEQ service, network support is essential. The LEQ architecture uses a few routers in the network as hubs to redirect packets of interactive applications along paths with similar end-to-end delay. We first formulate the hub selection problem, prove its NP-hardness, and provide a greedy algorithm to solve it. Through extensive simulations, we show that our LEQ architecture significantly reduces delay difference under different optimization criteria that allow or do not allow compromising the per-user end-to-end delay. Our LEQ service is incrementally deployable in today's networks, requiring just software modifications to edge routers.