input output from the mainframe 1 is feasible in the example of fig4 for example the snapshot of generation number 3 is utilizable in a system comprising a construction as described above the processing for acquiring snapshots of the ldev 30 a for each generation will be described with reference to the flow chart of fig5 first of all in the mainframe 1 in response to an instruction from an application 13 or an instruction from the user using an input device 10 a the snapshot management program 12 issues s 11 a snapshot acquisition command in respect of the disk array system 2 the snapshot acquisition command may include for example an address and generation number for specifying the main volume and auxiliary volume for example fig6 shows an example of the case where a snapshot acquisition command is input by the user on the command line 200 in this case on the command line 200 following the snapshot acquisition command the main volume address 210 the auxiliary volume address 220 and the generation number 230 are input thus the information that is input on the command line 200 is included in the snapshot acquisition command the control device 22 of the disk array system 2 receives this snapshot acquisition command the snapshot processing section 29 b then by referring to the generation management information 25 determines whether the address of the auxiliary volume that is contained in the snapshot acquisition command is registered in the ldev addresses 254 for each generation i e determines whether or not this address is already used s 12 if the.