High-resolution solid-state C-13 NMR spectra of (ethylene-vinyl alcohol) copolymers (EVOH) with various ethylene contents in the solid-state and their C-13 spin-lattice relaxation times, T-1, were measured, in order to elucidate the structure and dynamics of the copolymers. From these experimental results, the structural change of the EVOHs with changes of the ethylene content was successfully elucidated. Further, it is found that the C-13 T-1 for the CH carbon of the vinyl alcohol unit is mainly composed of two components. The fractions of short and long T-1 components increase and decrease with an increase in the ethylene fraction, respectively. From these experimental results, it can be said that changes of the ethylene content in the copolymers lead to large changes in their structure and dynamics.