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It is well known that compression and prediction are interrelated in that high compression implies good predictability, and vice versa. We use this correlation to find predictable properties of program behavior and apply them to appropriate cache management tasks. In particular, we look at two properties of program references: 1) Inter Reference Gaps: defined as the time interval between successive references to the same address by the processor, and 2) Cache Misses: references which access the next level of the memory hierarchy. Using compression, we show that these two properties are highly predictable and exploit them to improve Cache Replacement and Cache Prefetching, respectively.Using trace-driven simulations on SPEC and Dinero benchmarks, we demonstrate the performance of our predictive schemes, and compare them with other methods for doing the same. We show that, using our predictive replacement scheme, miss ratio in cache memories can be improved up to 43 percent over the well-known Least Recently Used (LRU) algorithm, which covers the gap between the LRU and the off-line optimal (MIN) miss ratios, by more than 84 percent. For cache prefetching, we show that our scheme eliminates up to 62 percent of the total misses in D-caches. An equivalent sequential prefetch scheme only removes up to 42 percent of the misses. For I-caches, our scheme performs almost the same as the sequential scheme and removes up to 78 percent of the misses.