Abstract: A method for detecting and remembering multiple sequential access patterns made from a host to a memory system having one or more logical storage devices. Once a sequential access pattern is detected, one or more tracks are requested to be prestaged ahead of the current access request. The number of tracks requested to be prestaged ahead may be responsive to the amount of storage available in the cache memory. One list is provided for each logical storage device. Each list has multiple entries and is logically divided into two parts. A sequential part contains entries for access streams which the system has determined are sequential and for which the system may have prestaged one or more tracks into cache. A candidate part contains information about recent host accesses which have not as yet been determined to be sequential. The entries within each of the two parts of the list are logically ordered in a most-recently-used fashion.