We use H-2 NMR to investigate the Segmental motion of poly(ethylene oxide) (PEO) in neat and nanocomposite materials that do and do not contain salt. Specifically, in addition to a neat low-molecular-weight PEO, we Study mixtures of this polymer with TiO2 nanoparticles and LiClO4. To characterize the polymer dynamics over a wide ran-e of time scales, we combine H-2 NMR spin-lattice relaxation, line-shape, and stimulated-echo analyses. The results consistently show that the presence of nanoparticles hardly affects the behavior of the polymer, while addition of salt leads to substantial changes; e.g., it reduces the crystallinity. For neat PEO and a PEO-TiO2 mixture, stmulated-echo spectroscopy enables measurement of rotational correlation functions for the crystalline phase. Analysis of the decays allows LIS to determine correlation times, to demonstrate the existence of a nonexponential relaxation, which implies a high complexity of the polymer dynamics in the crystal, and to show that the reorientation can be described as a large-angle jump. For a PEO-TiO2-LiClO4 mixture, we use H-2 and Li-7 NMR to study the polymer and the lithium dynamics, respectively. Analysis of the Li-7 spin-lattice relaxation reveals a high lithium ionic mobility in this nanocomposite polymer electrolyte. The Li-7 stimulated-echo decay is well described by a stretched exponential extending over about 6 orders of magnitude, indicating that a broad and continuous distribution of correlation times characterizes the fluctuations of the local lithium ionic environments.