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This paper aims at finding fundamental design principles for hierarchical Web caching. An analytical modeling technique is developed to characterize an uncooperative two-level hierarchical caching system where the least recently used (LRU) algorithm is locally run at each cache. With this modeling technique, we are able to identify a characteristic time for each cache, which plays a fundamental role in understanding the caching processes. In particular, a cache can be viewed roughly as a low-pass filter with its cutoff frequency equal to the inverse of the characteristic time. Documents with access frequencies lower than this cutoff frequency have good chances to pass through the cache without cache hits. This viewpoint enables us to take any branch of the cache tree as a tandem of low-pass filters at different cutoff frequencies, which further results in the finding of two fundamental design principles. Finally, to demonstrate how to use the principles to guide the caching algorithm design, we propose a cooperative hierarchical Web caching architecture based on these principles. Both model-based and real trace simulation studies show that the proposed cooperative architecture results in more than 50% memory saving and substantial central processing unit (CPU) power saving for the management and update of cache entries compared with the traditional uncooperative hierarchical caching architecture.