In a novel snapshot management method for a data storage system which does not use duplication (mirroring), when a snapshot of a main volume pertaining to a designated time is being taken, every time a write request to a storage region in the main volume is received, if the data in that storage region has not been copied to an auxiliary volume since the designated time, that data is copied to the auxiliary volume, and the writing to the storage region is carried out after that. In the case of sequential writing, also for data in a further storage region, following the target storage region, on which it is predicted that sequential writing will be carried out henceforth, if copying to the auxiliary volume has not been carried out since the designated time, the data is copied to the auxiliary volume in the same way.