A storage subsystem in which write data written in a first storage subsystem from a plurality of host computers is copied onto a second storage subsystem, thereby protecting the write data in a multiplex manner. Disclosed are a storage subsystem and its controlling method in which the first storage subsystem has a storage control unit which sets a first threshold for controlling for each of the host computers an occupancy ratio of the write data whose copy to the second storage subsystem is incomplete in a data buffer in the first storage subsystem, and has control logic for delaying the processing of a data write request from each of the host computers on the basis of the first threshold.