On the basis of the analysis of frequencies of occurence of pyrimidines of different length, the degree of clustering of DNA of a hundred species belonging to different taxons has been determined. A tendency towards increase in the index of DNA clustering was revealed in the sequence: bacteria, invertebrates, fishes, amphibians, reptiles, birds, mammals. A mechanism is postulated, according to which an increase in the degree of clustering of DNA in the process of progressive evolution of species may be due to accumulation of mutations, Pyr in equilibrium Pur transversions, resulting in an increase in the degree of asymmetry of the complementary chains of DNA. That this mechanism does exist is proved by a positive correlation between the degree of clustering of DNA and the degree of asymmetry of natural DNA chains. The mean frequency of mutation of vertebrates is about 4,6-10(-8) substitutions per nucleotide per year. Evolution of different groups of organisms may be accompanied with an increase in the rate of evolution of DNA structure. With the help of a special computer program, proceeding from the amino acid sequence of cytochromes c in 40 species belonging to different taxons, the degree of clustering of pyrimidines and the degree of asymmetry of complementary chains of DNA cistrons coding for cytochrome c was determined. A general tendency towards an increase in the mean values of the corresponding parametres of structure was found in the following: bacteria, invertebrates, fishes, amphibians, reptiles, birds and mammals. Thus, it was established that "neutral" amino acid substitutions in cytochromes are based on the selection of mutations leading to accumulation of pyrimidines in sense H-chain of DNA, and purines--in the corresponding mRNA. The frequency of mutation in cytochrome c of chordates is about 5,2-10(-8) of amino acid residues per year. It is assumed that the evolution modification of DNA structure may be due to increase in the disturbance stability of translation.