Abstract: Let {X_n,n≥1} be ρ^*mixing sequences with identical distributions belonging to the domain of the normal attraction with non-degenerate stable distribution. By means of the moment inequalities of the ρ^*mixing sequences, it was proved that probability 1 possesses,and some equivaent conditions were obtained.

Key words: ρ^*mixing sequences, Chover’s law of iterated logarithm, stable distribution