The correlation functions of the side - groups and side ?chains of polymers are obtained for nuclear spin relaxation if the segmental motion of the polymers is described by VJGM model, these functions are derived from unequal two ?side and three -site jump internal rotation, diffusion internal rotation, restricted internal rotation and multiple internal rotation. The corresponding spectral density functions are also given, and these functions are used to interpret the nuclear spin relaxation data of the side-groups of some polymers. The average spectral density functions of side-groups are derived under the magic angle spinning, the correlation times and diffusion coefficients of the side-groups of crosslinked poly (methyl methacry-latcs) and solid poly(vinylbutyral) are obtained by using these average spectral density functions. The multiphase structures of nylon 6, poly (ethylenc glycol) and its complexes are investigated with cross ?polarization and magic angle spinning techniques.Three methods using The correlation functions of the side - groups and side? Chains of polymers are obtained for nuclear spin relaxation if the segmental motion of the polymers is described by VJGM model, these functions are derived from unequal two? Side and three-site jump internal rotation, diffusion internal rotation, restricted internal rotation and multiple internal rotation. The corresponding spectral density functions are also given, and these functions are used to interpret the nuclear spin relaxation data of the side-groups of some polymers. The average spectral density functions of side- groups are derived under the magic angle spinning, the correlation times and diffusion coefficients of the side-groups of crosslinked poly (methyl methacry-latcs) and solid poly (vinylbutyral) are obtained by using these average spectral density functions. The multiphase structures of nylon 6, poly (ethylenc glycol) and its complexes are investigated with cross? Polarization and magic angle spinning techniques hree methods using