A computer system having a plurality of host computers and a storage system is provided which allows any one host computer to perform a global copy operation on any arbitrary or all storage areas in the storage system. To this end, storage areas provided by the disk devices are grouped into groups by allocating group numbers to a plurality of specified storage areas. The copy operation can be performed by specifying desired groups. Each of the groups is made up of sub-groups and the sub-groups are defined for each computer to assure a consistency of copy order of the sub-groups.