Measurements of the electrical conductivity and proton and fluorine-19 MMR spin-lattice relaxation times (T-1) in acid form NAFION 105, 117, and 120 conditioned at various levels of relative humidity have been carried out. Complex impedance studies were made along the plane of the polymer film at frequencies from 10 to 10(8) Hz at room temperature and pressures up to 0.3 GPa. The NMR measurements were made at room temperature and pressures up to 0.25 GPa. Both types of measurement were also carried out on various concentrations of sulfuric acid in water. The electrical conductivity decreases with increasing pressure for low water content acid solutions and low water content NAFION samples. This behavior (positive activation volumes) is that expected for "normal" liquids and for ions in polymers where the motion of the ions is determined by the host, matrix. However, for high water contents, the reverse is true. The electrical conductivity increases with increasing pressure which gives rise to a negative activation volume. The results show that at high water contents, the electrical conductivity mechanism in NAFION is essentially identical to that for a dilute acid where the transport is controlled by the aqueous component. The activation volumes extracted from the proton NMR T-1 data are in qualitative agreement with those obtained from the electrical conductivity measurements at intermediate and low water contents, suggesting that motion of the sulfonic acid-terminated pendant chains contributes to the conduction mechanism at low water contents.