A method for copying data from a source logical device to a destination logical device. In response to a copy command from a requesting host application identifying the source and destination logical 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 logical device during the copy phase. A copy program transfers the date on a track-by-track basis to the destination logical device. Procedures assure that any data access to a particular track in either the source or destination logical device by any application prior to the transfer of that track is accommodated to maintain data integrity.