A data processing system for allocating a plurality of peripheral storages to a plurality of users comprises a data processing device, a plurality of peripheral storages connected with the data processing device, a catalog control unit for setting on a table a total usage capacity of the usable space set by users including an active pool having a plurality of peripheral storages to which files are allocated and an inactive pool for holding files which are migrated from the active pool, a file allocating unit which sets the current usage capacity on a table depending upon the use of space of said active pool to compare the sum of the added space capacity inputted by users and the current usage capacity with said total usage capacity for deciding an error of allocation of the added peripheral storage when the sum is larger than the latter. A part of the peripheral storage in the active pool is set as spare volumes and the spare volumes are temporarily allocated when a failure occurs in the remaining part of the peripheral storages in the active pool or when there is not enough free space in the active pool.