The position annihilation in solids of alkali-metal fullerides with saturation composition; K6C60, Rb6C60 and Cs6C60 was found to consist of three processes with lifetimes of 0.21-0.24 ns, 0.60-0.75 ns and 3.2-3.7 ns at 300 K. The shortest and the intermediate lifetimes were almost independent of temperature, but the corresponding relative intensities were found to change with temperature in the range 290-480 K, which suggests that the distribution of positrons changes with temperature. The shortest lifetime is attributed to the annihilation of free positrons in the region where the wavefunctions of a positron and an electron overlap significantly, i.e., inside and around C-60 molecules in M(6)C(60) (M = K, Rb, Cs). The intermediate one is attributed to the annihilation of positrons at surfaces, and the longest one to that of ortho-positroniums.