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This paper investigates the optimal replication of data objects at hierarchical and transparent Web proxies. By transparent, we mean the proxies are capable of intercepting users' requests and forwarding the requests to a higher level proxy if the requested data are not present in their local cache. Two cases of data replication at proxies are studied: 1) proxies having unlimited storage capacities and 2) proxies having limited storage capacities. For the former case, an efficient algorithm for computing the optimal result is proposed. For the latter case, we prove the problem is NP-hard, and propose two heuristic algorithms. Extensive simulations have been conducted and the simulation results have demonstrated significant performance gain by using the proposed data replication algorithms and also shown the proposed algorithms out-perform the standard Web caching algorithm (LRU threshold method).