The ionic structure and transport properties of amorphous solid polymer electrolytes in the system copolymer of acrylonitrile and butadiene (40 : 60)—lithium hexafluoroarsenate (SPE) is studied in the region of small salt concentrations (up to 0.37 mol dm−3) at 298–368 K. In conditions studied, LiAsF6 is dissociated predominantly to ions. Macroscopic models of ion transport are used to analyze the results of measurements of transport characteristics of SPE. Transport of anions free of the polymer matrix is realized activationlessly and resembles the Stokes drift in viscous media. Transport of cations solvated by electron-donating groups of the polymer turns possible only at temperatures in excess of a critical value (T crit ≈ 333 K), when the statistical mean of molecules in the first coordination sphere of the lithium cation becomes less than four (which is the coordination number for solvation) and requires the overcoming of an energy barrier of ∼6 kJ mol−1. Below T crit, the SPE are unipolar anionic conductors.