Conductivity measurements have been made on solutions of the following substances in sulphuric acid: HClO4, HSO3F, HSO3Cl, HPO2F2, HAs(HSO4)4, CH3SO3H, and CF3CO2H. Of these substances HSO3F, HSO3Cl, HAs(HSO4)4, and probably HClO4, behave as acids, CF3CO2H is a non-electrolyte, and HPO2F2, and probably CH3SO3H, are bases of the sulphuric acid system. Acid dissociation constants for HSO3F, HSO3Cl, and HAs(HSO4)4have been determined by comparing the conductivities of their solutions with those of H2S2O7, whose dissociation constant is known from other measurements, and also by conductimetric titration with a strong base, e.g. KHSO4. These acids of the sulphuric acid system decrease in strength in the order HSO3F > HAs(HSO4)4 > HSO3Cl > HClO4.