1. Multi-processor system comprising: a shared storage for storing data; a plurality of storage controllers connected to said shared storage, each controller including a first buffer storage for storing data transmitted by said shared storage; and a plurality of processors, each of which is connected to an associated one of said storage controllers, each of said processors including a second buffer storage for holding data transmitted from said shared storage through said first buffer storage in said associated storage controller and a second directory for identifying the data stored in said second buffer storage for access to said second buffer storage; each of the storage controllers further comprises a first directory holding the address for identifying the data stored in the first buffer storage of that storage controller for access to said first buffer storage therein from an associated processor connected to the storage controller and a third directory for storing the same contents as the content stored in said second directory included in the associated processor, said first directory containing a plurality of entries, each entry containing an exclusive bit indicating whether the data existing in the corresponding first buffer storage is the only copy of the data from said shared storage which exists in any storage controller; and each of said storage controllers further comprises first means responsive to a store request from the associated processor for demanding data coincidence control to the the storage controllers, second means for transmitting the address accompanied by said store request only when the exclusive bit in an entry of the first directory relating to said first buffer storage, to which the store is requested, shows that it is not the only copy, third means responsive to a data coincidence control request and the address from the other storage controllers for invalidating the registration of said address in said first and third directories, and fourth means for demanding the invalidation of the address registration to the second directory of the processor relating to said third directory, in response to said address being registered in said third directory.