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Let {X n ; n ≥ 1} be a sequence of independent and identically distributed i.i.d. random variables and denote S n n k 1 X k , M n max 1≤k≤n X k. In this paper, we investigate the almost sure central limit theorem in the joint version for the maxima and sums. If for some numerical sequences a n > 0 , b n we have M n − b n /a n D → G for a nondegenerate distribution G, and f x, y is a bounded Lipschitz 1 function, then lim n → ∞ 1/D n n k 1 d k f S k / √ k, M k − b k /a k ∞ −∞ f x, y Φ dx G dy almost surely, where Φ x stands for the standard normal distribution function, D n n k 1 d k ,and d k exp log k α /k, 0 ≤ α < 1/2.

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