Stack processing, and in particular stack processing for the least recently used replacement algorithms, may present computational problems when it is applied to a sequence of page references with many different pages. This paper describes a new technique for LRU stack processing that permits efficient processing of these sequences. An analysis of the algorithm and a comparison of its running times with those of the conventional stack processing algorithms are presented. Finally we discuss a multipass implementation, which was found necessary to process trace data from a large data base system.