1. An address translation system in which a real space is shared by a plurality of logical spaces, comprising: a table base stack having a plurality of storage units, each storage unit storing a base address characteristic of a different virtual space, and each of said storage units having an identification flag characteristic thereof; a translation lookaside buffer for registering address translation pairs each consisting of a virtual address and a real address, which buffer has with respect to said translation pairs the identification parts in which the identification flags characteristic of said storage units of said table base stack are set; an output means for searching said storage units of said table base stack by using as a key a base address of a virtual space to be invalidated when an instruction is issued for invalidating an address translation pair in said translation lookaside buffer and for delivering the identification flag of the storage unit in which the desired base address is stored; a comparison means for sequentially reading said identification flags out of said identification parts of said translation lookaside buffer and comparing the read-out flags with signals from said output means; and means for purging the address translation pair corresponding to the identification part when the identification flag thereof produces a coincidence in the comparison performed by said comparison means.