A data processing system has files stored on disks in a tree structure of directories and files. The system is operated to rapidly open files which have been recently opened or for which partial path information is available, by accessing a drive cache (30) in main memory (16). The cache has entries chained in a tree structure which is then searched to provide the same information during the opening process as that information which would otherwise have to be obtained from a disk (22). When the cache is full, a new entry replaces the least recently used entry.