The solid solutions Li4-3xAlxGeO4 have a high conductivity which is independent of temperature above 700-degrees-C, e.g. 0.23-OMEGA-1 cm-1 for x = 0.10. A small fraction of the lithium ions appear to be in zero activation energy, liquid-like motion. Zero activation energy for ionic conduction is rare in crystalline materials and this is the first example observed for Li+ ions.