There is disclosed a data storage system used in a computer environment where there are plural host computers and plural storage array controllers. When a remote copy is made while assuring the order of writing across plural storage array controllers, one of the host computers gains copy information about all the storage array controllers associated with the remote copy as a representative. The representative one of the storage array controllers collects and stores copy statuses which are individually managed by the storage array controllers for which a remote copy is made. The host computer gains the copy statuses from the representative controller using an instruction to gain the copy statuses.