Tracks of data or other data units are copied from a primary storage system to a secondary storage system. For multiple-track or multiple-data unit transfers, a group of tracks or data units which are sequentially related are transferred. A respective task is defined at the primary storage system for monitoring a progress of the transfer of each of the respective data units in a group. A state is maintained for monitoring a progress of the transfer of the group responsive to the progress of each of the tasks. A normal state is selected when there are no failed tasks. A recovery state is selected when there is a failure, and the status of the remaining tasks is being ascertained. A retry state is selected following the recovery state to retry the failed tasks. A failed state indicates an unrecoverable failure.