Crystalline polymer electrolytes conduct, in contrast to the established view for 30 years. The crystalline polymer poly(ethylene oxide)6:LiXF6, X = P, As, Sb is composed of tunnels formed from pairs of (CH2-CH2-O)n chains, within which the Li+ ions reside and along which they may migrate. The anions are located outside the tunnels. PEO6:LiXF6 formed from PEO of average molecular weight 1000 Da has an average chain length of 40 A compared with a typical crystallite size of 2500 angstroms, hence low molecular weight materials have many chain ends within a crystallite. More chain ends increase conductivity. Materials composed of polydispersed PEO (chains of different lengths) of average molecular weight 1000 Da exhibit a conductivity one order of magnitude greater than monodispersed materials of the same molecular weight. Replacing the -OCH3 groups on the chain ends with -OC2H5 increases the conductivity by a further order of magnitude. Conductivity may also be increased by isovalent or aliovalent doping of the 6:1 complexes in which XF6- is replaced by N(SO2CF3)2- or SiF6(2-), respectively.