At 141 degrees C the solid acid CsHSO4 is known to undergo transition to a superprotonic phase that is characterized by dramatic (several-order-of-magnitude) increases in hydrogen ion conductivity. Proton NMR spin-spin relaxation time T-2 measurements reported here for CsHSO4 also reveal substantial increases (factors of 20-30) in the vicinity of the transition temperature. In the temperature range just below the transition (70-136 degrees C), T-2 increases by a factor of order 10 relative to the rigid-lattice regime, suggesting motional narrowing of the NMR resonance line. In the regime of motional narrowing, the activation energy barrier to diffusion is 0.40 eV, as determined from the present T-2 results. NMR spin-lattice relaxation T-1 measurements also show behavior consistent with transition to a regime of rapid hydrogen motion. In particular, proton T-1's decrease with temperature (from 80 to 120 degrees C), and then drop sharply near the transition temperature. Above the transition temperature, T-1 exhibits a minimum in which the correlation time is found to be similar to 2 ns. (C) 2005 Elsevier Ltd. All rights reserved.