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Proxy servers have been used to cache web objects to alleviate the load of the web servers and to reduce network congestion on the Internet. In this paper, a central video server is connected to a proxy server via wide area networks (WANs) and the proxy server can reach many clients via local area networks (LANs). We assume a video can be either entirely or partially cached in the proxy to reduce WAN bandwidth consumption. Since the storage space and the sustained disk I/O bandwidth are limited resources in the proxy, how to efficiently utilize these resources to maximize the WAN bandwidth reduction is an important issue. We design a progressive video caching policy in which each video can be cached at several levels corresponding to cached data sizes and required WAN bandwidths. For a video, the proxy server determines to cache a smaller amount of data at a lower level or to gradually accumulate more data to reach a higher level. The proposed progressive caching policy allows the proxy to adjust caching amount for each video based on its resource condition and the user access pattern. We investigate the scenarios in which the access pattern is priorly known or unknown and the effectiveness of the caching policy is evaluated.