Hydrogen-ion titration curves are reported for tomato bushy stunt virus, two strains of cowpea chlorotic mottle virus, and turnip crinkle virus, with particular attention to the hysteresis loops associated with the swelling and contraction of virions. There appears to be an archetypal shape of hysteresis loops, which is shared by viruses in several groups, suggestive of many intermediate states in the swelling of any one particle. In contrast, eggplant mosaic virus behaves as if its protein capsid is impermeable to small ions in mild conditions; its cation-binding sites were revealed by treatment with high concentrations of salt or urea, or at raised temperatures. Putting these observations together with the fact that a spherical virus capsid is a closed, holey, charged surface leads to a theory of titration hysteresis: its key feature is that the protein capsids of simple viruses are inherently semipermeable, with many of the ion-handling properties usually attributed only to complex lipid membranes.