In non-aqueous solvents, the S-6(2-) polysulfide ion is partly dissociated and is in equilibrium with the S-3(-) radical anion. Several electrochemical studies have considered the reduction of these polysulfides. However, it has not been possible to distinguish the reduction of S-3(-) from that of S-6(2-). In the present work we give the results of cyclic voltammetric experiments performed for Li2S6-NH3 solutions at various temperatures and scan rates. They show that, in liquid ammonia, S-3(-) is more easily reducible that S-6(2-). The experimental results lead to the conclusion that the kinetics of the equilibrium between S-6(2-) and S-3(-), which is strongly temperature dependent, play a key role in the reduction mechanism of S-3(-) and S-6(2-). The mechanism involves two one-electron transfer reactions leading to S-3(2-) and S-6(3-), coupled to an irreversible decomposition reaction of S-6(3-) into S-3(2-) and S-3(-). The proposed mechanism has been confirmed by numerical simulations that give an estimate of the reaction rate constants.