A model that may explain the limited division potential of certain cells such as human fibroblasts in culture is presented. The central postulate of this theory is that there exists, prior to certain key exons that code for materials needed for cell division, a unique sequence of specific repeating segments of DNA. One copy of such repeating segments is deleted during each cell cycle in cells that are not protected from such deletion through methylation of their cytosine residues. According to this theory, the means through which such repeated sequences are removed, one per cycle, is through the sequential action of enzymes that act much as bacterial restriction enzymes do--namely to produce scissions in both strands of DNA in areas that correspond to the DNA base sequence recognition specificities of such enzymes. After the first scission early in a replicative cycle, that enzyme becomes inhibited, but the cleavage of the first site exposes the closest site in the repetitive element to the action of a second restriction enzyme after which that enzyme also becomes inhibited. Then repair occurs, regenerating the original first site. Through this sequential activation and inhibition of two different restriction enzymes, only one copy of the repeating sequence is deleted during each cell cycle. In effect, the repeating sequence operates as a precise counter of the numbers of cell doubling that have occurred since the cells involved differentiated during development.