A method for copying data from a source disk storage device to a destination disk storage device. In response to a copy command from a requesting host application identifying the storage locations in source and destination disk storage devices, an environment is established. Thereafter a calling system receives an immediate response that the copy operation is complete even though no data has been copied. Application programs may access storage locations in either the source or the destination disk storage device during the copy phase. A copy program transfers the date on a track-by-track basis to the storage locations in the destination disk storage device. Procedures assure that any data access to a particular track in either the source or destination disk storage devices by any application prior to the transfer of that track are accommodated to maintain data integrity.