Analysis for the homogeneity of the distribution of the second base of dinucleotides in relation to the first, whose bases are separated by 0, 1, 2,... 21 nucleotide sites, was performed with the VIH-1 genome (cDNA), the Drosophila mtDNA, the Drosophila Torso gene and the human p-globin gene. These four DNA segments showed highly significant heterogeneities of base distributions that cannot be accounted for by neutral or nearly neutral evolution or by the "neighbor influence" of nucleotides on mutation rates. High correlations are found in the bases of dinucleotides separated by 0, 1 and more number of sites. A periodicity of three consecutive significance values (measured by the x²9) was found only in Drosophila mtDNA. This periodicity may be due to an unknown structure or organization of mtDNA. This non-random distribution of the two bases of dinucleotides widespread throughout these DNA segments is rather compatible with panselective evolution and generalized internucleotide co-adaptation.