A cache memory (26) is contained in a processor (1) which features a high efficiency in spite of its small capacity. In the cache memory control circuit of the invention, it is detected whether the access operation of the processor is directed to a particular region of the memory, and when the data is to be read out from, or is to be written onto, the particular region, the data is copied onto the cache memory (26) and when the data is to be read out from other regions, operation of the memory is executed immediately without waiting for the reference of cache memory. By assigning the particular region for the data that are to be used repeatedly, it is possible to obtain a cache memory (26) having good efficiency in spite of its small capacity. A representative example of such data is the data in a stack.