Using gene genealogies constructed from gene sequence data, we show that both the mucosal and cutaneous papillomaviruses (PV)-supergroups A and B-appear to have been transmitted through susceptible populations faster than exponentially. The data and methods involved (1) examining the PV database for phylogenetic signal in an L1 open reading frame (ORF) fragment and an E1 ORF segment, (2) demonstrating that the same two fragments have evolved in a way consistent with a molecular clock, and (3) applying methods of phylogenetic tree analysis that test different scenarios for the dynamics of viral transmission within populations. The results indicate increases in PV populations of both supergroups A and B in the recent past. This form of the increases, which fit a null model of population growth with an exponent increasing in time, is compatible with the fact that human populations have grown at a faster than exponential rate, thus increasing the numbers of susceptible hosts for HPVs. There are, however, indications that the population of supergroup A has now stopped increasing in size.