Solid-state nuclear magnetic resonance spectroscopy and relaxation measurements, together with DSC, have been used to elucidate the structures and molecular dynamics in poly(ethylene-co-vinyl acetate) (EVA). It has been found that besides immobile orthorhombic and monoclinic crystalline phases, the third mobile crystalline phase (possibly the phase) of a considerable amount (36% of total crystalline phases) appears in the EVA samples, which forms during room-temperature aging as a result of the secondary crystallization and melts at temperature somewhat higher than room temperature. Such a mobile crystalline phase has not only the well-defined chemical shift of its own, but also has different molecular mobility from the orthorhombic phase. The mobile crystalline phase is characterized by the rapid relaxation of the longitudinal magnetization, which is caused by conventional spin-lattice relaxation, while the slow relaxation of the longitudinal magnetization occurring in the orthorhombic phase is originated from the chain diffusion. In addition, the amorphous phase also contains two components: an interfacial amorphous phase and a melt-like amorphous phase.