Our own and literary data about antimutagenic role of autonomous 3'-->5'-exonucleases (AE) are analyzed. AE are not bound covalently to DNA polymerases but often involved in replicative complexes. Intracellular overproduction of AE in bacteria is accompanied with the sharp suppression of mutagenesis, whereas the inactivation of AE in bacteria and higher fungi results in the increase of mutation rates by 2-3 orders of magnitude. The addition of AE in biologically meaningful concentrations to DNA polymerases elevates substantially the accuracy of their work in vitro. In these cases, the reverse mutation rates were measured in the DNA from phage (X174 amber 3, whereas the direct mutation rates--in the DNA from phage M13mp2, both being used as primer-templates for DNA synthesis and then transfected into spheroplasts of Escherichia coli. The accuracy of action of nuclease-free DNA polymerases alpha and beta are shown to raise in the presence of AE by 2-3 orders, the accuracy of moderately processive DNA polymerase I--by 2 orders, the accuracy of highly processive DNA polymerase delta--by 5-10 times, though the latter 2 polymerases display and their own 3'-->5'-exonucleolytic activity. AE, involved in the multienzyme DNA polymerase complexes, augment the accuracy of complexes action by 5-10 times. The model of "external" corrective role of AE in DNA biosynthesis is proposed. Study of 30 objects from all 3 kingdoms of live beings (from archae- and eubacteria to mammalia including human) has shown that AE account, as minimum, from 30 to 90% of the total cellular 3'-->5'-exonucleolytic activity. So AE increase essentially the intracellular ratio of values of 3'-->5'-exonuclease to DNA polymerase activities in the very various representatives from a phylogenetic tree that results always in the augmentation of the accuracy of DNA biosynthesis.