The problem of sex origin of eukaryotes in the process of evolution still has not settled. Existing theories and hypothesizes mainly concern the maintenance and biological reasonability of sexual mode of replication. Their theoretic foundation is based on Darwin’s and Mendel’s ideas that sex was originated due to natural selection and genes. Another model is proposed – sex of eukaryotes was originated as a result of long-term evolution of non-coding DNAs in a genome at one of the branches of prokaryotes. Non-coding DNAs accumulation and evolution in prokaryotes’ ring chromosomes eventually led to emergence of mitotic chromosomes and mitotic way of cell division. Sex and sexual replication became possible since that time when modified variant of mitosis – meiosis – have originated. Separate stages of the proposed model may be exposed to experimental check.