Based on 152 mitochondrial genomes and 36 bacterial chromosomes that have been completely sequenced, as well as three long contigs for human chromosomes 6, 21, and 22, we examined skews of mononucleotide frequencies and the relative abundance of dinucleotides in one DNA strand. Each group of these genomes has its own characteristics. Regarding mitochondrial genomes, both CpG and GpT are underrepresented, while either GpG or CpC or both are overrepresented. The relative frequency of nucleotide T vs A and of nucleotide G vs C is strongly skewed, due presumably to strand asymmetry in replication errors and unidirectional DNA replication from single origins. Exceptions are found in the plant and yeast mitochondrial genomes, each of which may replicate from multiple origins. Regarding bacterial genomes, the "universal" rule of CpG deficiency is restricted to archaebacteria and some eubacteria. In other eubacteria, the most underrepresented dinucleotide is either TpA or GpT. In general, there are significant T vs A and G vs C skews in each half of the bacterial genome, although these are almost exactly canceled out over the whole genome. Regarding human chromosomes 6, 21, and 22, dinucleotide CpG tends to be avoided. The relative frequency of mononucleotides exhibits conspicuous local skews, suggesting that each of these chromosomal segments contains more than one DNA replication origin. It is concluded that, when there are several replicons in a genomic region, not only the number of DNA replication origins but also the directionality is important and that the observed patterns of nucleotide frequencies in the genome strongly support the hypothesis of strand asymmetry in replication errors.