The quasielastic neutron scattering spectra of aqueous solutions of sulphuric acid have been recorded and compared to those of pure water and of caesium sulphate solutions in order to study the proton dynamics in these systems and in particular the abnormal proton diffusivity expected to occur in acidic solution. Mean transport coefficients for the water molecules' translational and rotational diffusive motions have first been determined in the three systems. They indicate a marked slowing down of the translational diffusion when salt or acid are added to water. The rotational motion is much less affected. In H2SO4 solutions corresponding to the maximum of specific conductivity, some evidence is obtained for a weak and broad quasielastic component, not present in pure water or in Cs2SO4 solutions. Its analysis is reasonably accurate only for momentum transfer values Q lower than 0·5 A-1. In this low Q limit, the rotational contributions can be neglected and the spectra of the acidic solutions can simply b...