One embodiment provides a computer system and data backup method which enable improvements in the response performance of a storage apparatus to a write request from a host apparatus. In a case where, during execution of same intra-enclosure copy processing, a primary storage apparatus receives a write request in which the data write destination is a storage area in a target range for the same intra-enclosure copy processing in a first primary volume in the primary storage apparatus, the primary storage apparatus transmits an advance notification storing an address of a storage area in a secondary storage apparatus which corresponds to the data write destination storage area designated in the write request to the secondary storage apparatus such that an on-demand copy is executed based on the advance notification in the secondary storage apparatus.