one or more disk devices making up a plurality of storage areas, said storage areas being under control of a plurality of computers; and

a storage controller connecting the plurality of computers and said storage areas, and receiving an input/output (I/O) access from the plurality of computers;

said plurality of computers accessing said storage areas such that each of said computers accesses predetermined ones of said storage areas without being permitted to access others of said storage areas being accessed by others of said plurality of computers;

wherein the storage controller holds copy group information for allocating groups to sets of selected said storage areas as objects to be copied to other storage areas in other disk devices connected to another storage controller via a communication line and including copy group names allocated to the groups,

each of the copy groups is made up of sub-copy groups and each of said copy groups is predetermined according to a desired requirement regarding objects to be copied, and the sub-copy groups are defined to correspond to the predetermined ones of said storage areas for each of the plurality of computers that make an IO access;

each of the copy groups has a consistency assurance level defining an order in which data is updated that is one of sub-group assured in which consistency is assured for all said storage areas in the sub-copy group, completely assured in which consistency is assured for all said storage areas in the copy group or unassured;

the storage controller receives, from any of the plurality of computers, an instruction which designates one among the copy groups in the form of a copy group name, and performs a copy operation for the designated copy group of the storage areas on the basis of the instruction, including determining whether the copy operation is an asynchronous remote copy operation, and when it is determined that the copy operation is an asynchronous remote copy operation, checking a consistency assurance level for the designated copy group to determine if the designated copy group is completely assured, sub-copy group assured or unassured;

assigning a corresponding consistency group number based on the determined consistency assurance level before performing the copy operation; and when a fault occurs in the copy operation of the copy group, suspending the copy operation for all of the storage areas of the designated copy group or suspending the copy operation for all of the storage areas for the sub-copy group associated with the fault in accordance with the consistency group number of the designated copy group.