Oxygen permeability and the free-volume hole size (cavity size) of ethylene-vinylalcohol copolymers (EVOH) indicate abnormal humidity dependence, that is, they have minimum values in the range of around 20-40% RH, not showing a monotonic increase with humidity. To clarify this abnormal phenomenon, we investigated its molecular mobility and amorphous structure change by means of solid-state NMR and temperature-modulated differential scanning calorimetry (TMDSC). The glass transition temperature (T-g) decreased with humidity. Specimens stored at 15-60% RH showed large enthalpy relaxation, and it was found that the amorphous structure became more compact and the molecular conformation became more stable by ageing within this range of humidity. Under these conditions, solid-state NMR measurement showed a component with intermediate relaxation time in the amorphous region. The results obtained by TMDSC and solid-state NMR showed a reduction in molecular mobility by densifying in the amorphous region under the condition of 15-60% RH. The fact that the oxygen permeability and the cavity size of EVOH indicate minimum values at low humidity are attributed to the reduction in molecular mobility by enthalpy relaxation. (C) 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1181-1191, 2009