To an approximation Chargaff's rule (%A = %T; %G = %C) applies to single-stranded DNA. In long sequences, not only complementary bases but also complementary oligonucleotides are present in approximately equal frequencies. This applies to all species studied. However, species usually differ in base composition. With the goal of understanding the evolutionary forces involved, I have compared the frequencies of trinucleotides in long sequences and their shuffled counterparts. Among the 32 complementary trinucleotide pairs there is a hierarchy of frequencies which is influenced both by base composition (not affected by shuffling the order of the bases) and by base order (affected by shuffling). The influence of base order is greatest in DNA of 50% G + C and seems to reflect a more fundamental hierarchy of dinucleotide frequencies. Thus if TpA is at low frequency, all eight TpA-containing trinucleotides are at low frequency. Mammals and their viruses share similar hierarchies, with intra- and intergenomic differences being mainly associated with differences in base composition (percentage G + C). E. coli and, to a lesser extent, Drosophila melanogaster hierarchies differ from mammalian hierarchies; this is associated with differences both in base composition and in base order. It is proposed that Chargaff's rule applies to single-stranded DNA because there has been an evolutionary selection pressure favoring mutations that generate complementary oligonucleotides in close proximity, thus creating a potential to form stem-loops. These are dispersed throughout genomes and are rate-limiting in recombination. Differences in (G + C)% between species would impair interspecies recombination by interfering with stem-loop interactions.