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Our goal is to state and prove the almost sure central limit theorem for maxima ( M n  ) of  X  1 ,  X  2 , ...,  X n  ,  n  ∈ ℕ, where ( X i  ) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed  n , the family of r.v.’s ( X  1 , ..., X n  ) has the Archimedean copula  C  Ψ .

Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima