By employing a palladium-hydrogen electrode it is possible to inject protons into single crystals of Li2SO4H2O. As predicted by Maricic et al. migration of protons is much preferred along the b axis of the monoclinic crystal. The current-voltage characteristics for this direction, and for the other two major directions, are interpretable in terms of space-charge-limited-currents, and, using the equations valid under such conditions the effective mobility (assumed to be field-independent) is estimated to be ca 10–7 to 10–8 cm2 V–1 s–1. Lower limits for the trap concentration are in the range 1012–1013 cm–3, and the number of effective charge carriers is about 1011 cm–3. From an examination of the structure of the solid, it is possible to formulate a plausible mechanism, based on Grotthuss conduction, for the preferred migration of the protons.