When plural copy groups including pairs exist, remote copying for pairs belonging to copy groups is suspended selectively on a copy group-to-copy group basis, instead of suspending remote copying in all the copy groups at once. A computer system has a host computer, plural first storage systems comprising plural first logical disks, and plural second storage systems comprising plural second logical disks. A first logical disk and a second logical disk paired with the first logical disk, and each pair belongs to either a first copy group or a second copy group. To selectively suspend remote copying on a copy group-to-copy group basis, one of the copy groups is specified first and then pairs belonging to this copy group are designated. The first storage systems comprising first logical disks of the designated pairs suspend remote copy processing for the designated pairs.