Hydrogen-ion transport numbers, water transference numbers, and acid absorption are reported for some cation-exchange membranes in presence of 0.1N, 1.0N, and 5.0N sulphuric acid. The transport numbers of hydrogen ion remain fairly close to unity even at the highest acid concentration; this is largely due to the retardation of the anions by the electro-osmotic water flux. With increasing acid concentration the water transference number falls to a lower limit of 1.0 mole per faraday; with the driest membrane used this value is obtained at all acid concentrations used. This behaviour suggests that when there are less than about 11 moles of water available per hydrogen ion in the membrane, association occurs between sulphonate groups and hydrogen ions, with consequent immobilization of the latter.