Polymer electrolytes have been studied extensively because uniquely they combine ionic conductivity with solid yet flexible mechanical properties, rendering them important for all-solid-state devices including batteries, electrochromic displays and smart windows(1-3). For some 30 years, ionic conductivity in polymers was considered to occur only in the amorphous state above T(g). Crystalline polymers were believed to be insulators. This changed with the discovery of Li(+) conductivity in crystalline poly(ethylene oxide)(6):LiAsF(6) (refs 4, 5). However, new crystalline polymer electrolytes have proved elusive, questioning whether the 6: 1 complex has particular structural features making it a unique exception to the rule that only amorphous polymers conduct. Here, we demonstrate that ionic conductivity in crystalline polymers is not unique to the 6: 1 complex by reporting several new crystalline polymer electrolytes containing different alkali metal salts (Na(+), K(+) and Rb(+)), including the best conductor poly(ethylene oxide)(8):NaAsF(6) discovered so far, with a conductivity 1.5 orders of magnitude higher than poly(ethylene oxide)(6):LiAsF(6). These are the first crystalline polymer electrolytes with a different composition and structures to that of the 6: 1 Li(+) complex.