A memory system is disclosed which includes a large main memory having information block storage locations addressable by an address consisting of set and tag bits, two buffer memory banks each having storage locations addressable by the set bits for the storage of tags and associated information blocks, and a small content-addressed memory for the storage of associated tags, sets, and information blocks. Initially, all information blocks are in the main memory, and accessing an information block results in a transfer of the block with its tag to one or the other of the buffer memories at a location determined by the set bits. Later, when another information block belonging to the same set is accessed, it is stored in the other buffer memory bank. Subsequently, when a third information block of the same set is accessed, one of the information blocks is displaced from the buffer memory bank to the content-addressed memory where it is stored with its tag and set bits. The system operates so that there is a high probability that a desired information block will be present and rapidly accessible in one of the buffer memory banks or the content-addressed memory.