1. In a machine-effected method of managing data storage space in a cache arranged to store data in addressable pages for casting out pages of stored data to be replaced by new data, a backing store connected to the cache for storing said pages of data in a plurality of addressable continuation chains, each of said addressable continuation chains having a plurality of said pages of data stored in respective addressable data storage areas of said backing store; machine-executed steps of: in said cache, storing said pages of data in a plurality of sets, each of said sets storing pages of data from respective ones of said continuation chains in said backing store; in said cache, for each said set, first indicating, in a sequence indication, a sequence of storing in said cache said pages of each of said sets for indicating in each of said sets a last stored one of the pages in the respective sets; in the cache, second indicating that a page of data is to be cast out of said cache; responding to said second indicating step for first identifying a first one of said sets stored in said cache from which a page is to be selected for cast out form said cache; then, first examining said sequence indication of said first one of said sets for identifying said last stored page in said first one of said sets as a cast out page; then, casting out said cast out page from said first one of said sets; establishing first and second addressing procedures for accessing said sets; selecting said first procedure for primarily sequential page accessing and selecting said second procedure for randomly accessing said sets; maintaining an indication of the access procedure last used in accessing the page sin all of said sets in said cache; in third identifying step, determining from said maintained indication which of said cache accessing procedures was used to access a page of data in said cache; if said second cache accessing procedure was last used to access a page of data in said cache, then second identifying a second one of said sets that is storing pages of data that contains pages of data to be candidates to be cast out of said cache; determining which of said pages of data is a least recent used page of said second one of said sets, then selecting said least recent used page in said second set to be said cast out page; if said first addressing procedure was least used, then performing said first examining step; in said first accessing procedure using a hash table to address pages in the cache; in said second accessing procedure using a directory tree to address pages in the cache; attempting to store a new data page into the cache, detecting that the cache is full of data; then in response to detecting said cache is full of data, indicating a page fault; in response to indicating a page fault, performing said first identifying step that identifies a page of data to be cast out, then performing said first examining step and said casting out step; then storing said new page of data in said cache; in said attempting to store step, generating an address of a predetermined one of said addressable continuation chains in said backing store storing said new page for addressing said predetermined one of said addressable continuation chains; examining predetermined ones of said sets in the cache for identifying a predetermined one of said examined sets to receive and store said new page of data; then identifying said predetermined one of said examine sets to be said first one of said sets for casting out a last stored page from said first one of said sets and then storing the new page in said first one of said sets; otherwise, identifying said least recent accessed set to be said second set, then establishing a new set in said cache for receiving and storing said new page of data.