Proton dynamics in phase I of CsHSO4 have been studied by means of III spin-lattice relaxation. From the analysis of the relaxation times, mean residence times of protons are estimated. Translational diffusion of protons takes place with parameters of E-a = 3 5 kJ/mol and tau(0) = 1.7 x 10(-13) s. The proton mean residence time changes from 3.0 x 10(-9) to 1.3 x 10(-9) s in the temperature range from 430 to 470 K. These parameters can well explain the macroscopic electric conductivity. The proton transfer between two SO4 tetrahedra along a hydrogen bond is fast enough and the proton transport is limited by the SO4 reorientation in a similar manner to phase II. (C) 2004 Elsevier B.V. All rights reserved.