Infections with hepatitis B and C viruses (HBV, HCV) are widespread in human populations throughout the world, and are major causes of chronic liver disease and liver cancer. HBV, HCV and the related hepatitis G virus or GB virus C (referred to here as HGV/GBV–C) are capable of establishing persistent, frequently lifelong infections characterized by high levels of continuous replication. All three viruses show substantial genetic heterogeneity, which has allowed each to be classified into a number of distinct genotypes that have different geographical distributions and associations with different risk groups for infection. Information on their past transmission and epidemiology might be obtained by estimation of the time of divergence of the different genotypes of HCV, HBV and HGV/GBV–C using knowledge of their rates of sequence change. While information on the latter is limited to short observation periods and is therefore subject to considerable error and uncertainty, the relatively recent times of origin for genotype of each virus predicted by this method (HCV, 500–2000 years; HBV, 3000 years; HGV/GBV–C, 200 years) are quite incompatible with their epidemiological distributions in human populations. They also cannot easily be reconciled with the recent evidence for species–associated variants of HBV and HGV/GBV–C in a range of non–human primates. The apparent conservatism of viruses over long periods implied by their epidemiological distributions instead suggests that nucleotide sequence change may be subject to constraints peculiar to viruses with single–stranded genomes, or with overlapping reading frames that defy attempts to reconstruct evolution according to the principles of the ‘molecular clock’. Large population sizes and intense selection pressures that optimize fitness may be additional factors that set virus evolution apart from that of their hosts.