C-13 NMR NT1 and NOE have been calculated by using composite spectral density functions describing polymer chain segmental motion and internal rotation of a hydrocarbon side chain attached to the polymer backbone. Numerical results at two magnetic fields are presented as a function of the various motional parameters characterizing the various models. NT1 and NOE relaxation parameters are well behaved and appear to have practical value for describing the dynamics of these systems. The models have been applied to the relaxation data of poly(n-butyl methacrylate) and poly(n-hexyl methacrylate) in toluene solutions. The dynamics of the two polymers are characterized by a very localized backbone motion and restricted internal rotation about successive C-C bonds of the side chains.