Since DNA polymerase requires a labile primer to initiate unidirectional 5'-3' synthesis, some bases at the 3' end of each template strand are not copied unless special mechanisms bypass this "end-replication" problem. Immortal eukaryotic cells, including transformed human cells, apparently use telomerase, an enzyme that elongates telomeres, to overcome incomplete end-replication. However, telomerase has not been detected in normal somatic cells, and these cells lose telomeres with age. Therefore, to better understand the consequences of incomplete replication, we modeled this process for a population of dividing cells. The analysis suggests four things. First, if single-stranded overhangs generated by incomplete replication are not degraded, then mean telomere length decreases by 0.25 of a deletion event per generation. If overhangs are degraded, the rate doubles. Data showing a decrease of about 50 base-pairs per generation in fibroblasts suggest that a full deletion event is 100 to 200 base-pairs. Second, if cells senesce after 80 doublings in vitro, mean telomere length decreases about 4000 base-pairs, but one or more telomeres in each cell will lose significantly more telomeric DNA. A checkpoint for regulation of cell growth may be signalled at that point. Third, variation in telomere length predicted by the model is consistent with the abrupt decline in dividing cells at senescence. Finally, variation in length of terminal restriction fragments is not fully explained by incomplete replication, suggesting significant interchromosomal variation in the length of telomeric or subtelomeric repeats. This analysis, together with assumptions allowing dominance of telomerase inactivation, suggests that telomere loss could explain cell cycle exit in human fibroblasts.