In eukaryotes, DNA damage tolerance (DDT) can be achieved through two mechanisms. One mechanism is mediated by the homologous recombination repair proteins. The other is under control of the RAD6 epistatic group genes and is divided into two more pathways, including error-free and error-prone ones. The error-prone mechanism, termed translesion DNA synthesis (TLS), is carried out with the participation of specialized TLS DNA polymerases. TLS is an important source of mutational changes in DNA. On the contrary, upon the realization of RAD6-dependent error-free DDT mechanism, relatively higher accuracy of DNA synthesis is provided by the use of intact sister chromatid or a homologous chromosome as a template to continue replication. In this case, after the replication fork stalling at the site of damage, the 3' end of the synthesized strand is transferred to an intact homologous DNA molecule, the synthesis continues for some length on a new template, and then the elongated strand is transferred back to the original chromatid. Inactivation of most genes that control the error-free DDT mechanism either does not affect the level of UV-induced mutagenesis or decreases it. Exceptions include genes belonging to the HSM3 epistatic group. Mutations in the genes of this group lead to a considerable increase in the frequency of UV-induced mutagenesis. This review focuses on the error-free DDT pathway, and attempts to substantiate the role of the HSM3 epistatic group genes in a series of molecular events that lead to the error-free bypass of replication-blocking lesions in budding yeast are made.