Let {Xn(t), t ∈ [0, ∞)}, n ∈ N, be standard stationary Gaussian processes. The limit distribution of supt∈[0,T(n)] |Xn(t)| is established as rn (t), the correlation function of {Xn (t), t ∈ [0, ∞)}, n ∈ N, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).