Electrical conductivities were measured at temperatures ranging 170-400 K for several composite materials in which alpha-AgI was frozen by twin-roller rapid quenching in the AgI-Ag2O-M(x)O(y) (M(x)O(y) = B2O3 and MoO3) glass matrices. In all the systems, the composite materials exhibited much larger activation energies E(a) for conduction at lower temperatures compared with those at room temperature. The E(a) values were steeply decreased from approximately 30 to approximately 20 kJ mol-1 at around 270 K on heating process. The larger E(a) values at lower temperatures were attributable to a positional ordering of Ag+ ions in the frozen alpha-AgI in the composite materials. Such an ordering of Ag+ ions was probably caused by the lattice strain produced in the alpha-AgI microcrystals because the strain was found to be much larger at temperatures below 270 K on the basis of low-temperature X-ray diffraction measurements for the composite materials.