A data processing system has a hierarchical storage system comprising first and second storage levels, the second storage level being of larger size and slower access time than the first level. For example, the first level comprises a magnetic fixed disk store and the second level comprises an optical disk jukebox. Each level holds a number of data sectors. Sectors are staged from the second storage level to the first storage level when required, and least recently used data sectors are pre-staged from the first storage level to the second storage level, in advance of their deletion from the first storage level. Previously pre-staged sectors are deleted from the first storage level only when space is required in the first storage level for staging in one or more sectors from the second storage level. Thus, staging and prestaging are performed on the basis of data sectors, rather than files.
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