A non-shared system with respect to an outside and an inside cache in a multi-processor system has multi-layer hierarchical cache. An invalidation address on a main memory address bus 31 in company with the rewriting of a main memory 30 is transmitted via a first and a second path 35, 36 to inside caches 11,21 so as to invalidate these inside caches 11, 21. The invalidation address is transmitted to the outside caches 12, 22 via the bidirectional connections between the main memory address bus 31 and outside caches 12, 22 so as to invalidate these outside caches 12, 22. It is extremely improbable for the address of access for writing to the transmitted to the main memory address bus 31 because the outside caches 12, 22 are operated in either copy back or write once system. As a result, even though the invalidation address is transmitted to the outside caches 12, 22 via the bidirectional connections between the main memory address bus 31 and the outside caches 12, 22, it is extremely improbably for the address of access for writing to conflict with a signal on the bidirectional connection.