There is now strong experimental evidence that epithelial stem cells arrange their sister chromatids at mitosis such that the same template DNA strands stay together through successive divisions; DNA labeled with tritiated thymidine in infancy is still present in the stem cells of adult mice even though these cells are incorporating (and later losing) bromodeoxyuridine [Potten, C. S., Owen, G., Booth, D. & Booth, C. (2002) J. Cell Sci.115, 2381-2388]. But a cell that preserves "immortal strands" will avoid the accumulation of replication errors only if it inhibits those pathways for DNA repair that involve potentially error-prone resynthesis of damaged strands, and this appears to be a property of intestinal stem cells because they are extremely sensitive to the lethal effects of agents that damage DNA. It seems that the combination, in the stem cell, of immortal strands and the choice of death rather than error-prone repair makes epithelial stem cell systems resistant to short exposures to DNA-damaging agents, because the stem cell accumulates few if any errors, and any errors made by the daughters are destined to be discarded. This paper discusses these issues and shows that they lead to a model that explains the strange kinetics of mutagenesis and carcinogenesis in adult mammalian tissues. Coincidentally, the model also can explain why cancers arise even though the spontaneous mutation rate of differentiated mammalian cells is not high enough to generate the multiple mutations needed to form a cancer and why loss of nucleotide-excision repair does not significantly increase the frequency of the common internal cancers.