Abstract: A cache memory hierarchy having a first level write through cache memory and a second level write back cache memory is provided to a computer system having a CPU, a main memory, and a number of DMA devices. The first level write through cache memory responds to read and write accesses by the CPU, and snoop accesses by the DMA devices, whereas the second level write back cache memory responds to read and write accesses by the CPU as well as the DMA devices. Additionally, the first level write through cache memory is a relatively large cache memory designed to provide a high cache hit rate, whereas the second level write back cache memory is a relatively small cache memory designed to reduce accesses to the main memory. Furthermore, the first level write through cache memory reallocates its cache lines in response to CPU read misses only, whereas the second level write through cache memory reallocates its cache lines in response to CPU write misses only.