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This work is devoted to the analysis of page replacement algorithms under assumptions on the stochastic nature of the sequence of memory accesses. A detailed discussion of the authors' results, some of which were published in Russian, and their relations to other papers is given. The object of study of this paper is two families of page replacement algorithms (PRA's) which contain certain algorithms of practical and theoretical interest. Analytical results are derived using the assumption that the references to the pages are independent identically distributed (iid) random variables. The algorithms of the first family are intervening between FIFO and LRU and the algorithms of the second family estimate the most frequently referenced pages considerably better than LRU. Explicit expressions of the page fault probabilities are obtained for these families and least upper bounds of performance are established which are independent of the page request probabilities. It is shown that for the second family the fault probabilities are less than twice the optimal one.