Mutations in the genes of corrective 3' --> 5'-exonucleases as well as in DNA polymerases lead to decrease in DNA biosynthesis accuracy all over genome. This is accompanied by the increase in mutagenesis and carcinogenesis probabilities. In this work, the activities of 3' --> 5'-exonucleases and DNA polymerases were studied in the extracts from normal and cancer cells of rodents and humans, and we are the first to measure their integral ratios. As example, in cultivated dermal fibroblasts of an adult human, the value of the ratio of activities of 3' --> 5'-exonucleases to DNA polymerase activity (3'-exo/pol) surpassed several folds the such a value for HeLa cells. Similar picture was observed during the comparison of normal fibroblasts of rat embryos and transformed fibroblasts of Chinese hamster A238. Experiments with cell-free extracts of some organs from healthy rats of various ages have shown that normal proliferating cells demonstrate higher 3' --> 5'-exonuclease activity and higher values of 3'-exo/pol that quiescent cells. Comparison of these data suggests a violation of the function of corrective 3' --> 5'-exonucleases in abnormally growing cancer cells.