We have studied the low‐temperature NMR line shape for three nuclei (¹H, ⁷Li, and ¹⁹F) in poly(ethylene oxide)‐lithium salts (LiClO₄, LiBF₄, and LiAsF₆) solid polymer ionic conductors and measured their spin–lattice relaxation rates as functions of frequency and temperature. The three nuclei probe the dynamics of the polymer segments, the cations, and the anions. We find that the Li⁺ cations follow the segmental motion of the chain, while the anions move independently. Homonuclear interactions and heteronuclear interactions with the polymer and the anion contribute to the ⁷Li line shape. When the heteronuclear contributions were selectively eliminated by the decoupling method, it was found that the Li–H interaction accounts for 80%–90% of the linewidth. Additional evidence for the correlation between the cationic and the polymeric motions is provided by the remarkably similar temperature dependences of the measured relaxation rates for ⁷Li and ¹H, which differ significantly from the dependence for ¹⁹F. The frequency dependence of the relaxation rates is poorly described by the Bloembergen, Purcell, and Pound model; a recently developed graphical procedure nevertheless shows that the motion of the protons and the anions is governed by a single time scale, while the ⁷Li ions are affected by an additional scale, associated with the coupling of its quadrupolar moment to the electric‐field gradient.