One of the primary motivations for implementing virtual memory is its ability to automatically manage a hierarchy of storage systems with different characteristics. The composite system behaves as if it were a single-level system having the more desirable characteristics of each of its constituent levels. In this paper, we extend the virtual memory concept to within each of the levels of the hierarchy. Each level is thought of as containing two additional levels within it. This hierarchy is not a physical one, but rather an artificial one arising from the employment of two different replacement algorithms. Given two replacement algorithms, one of which has good performance but high implementation cost and the other poor performance but low implementation cost, we propose and analyze schemes that result in an overall algorithm having the performance characteristics of the former and the cost characteristics of the latter. We discuss the suitability of such schemes in the management of storage hierarchies that lack page reference bits.