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Let {Xni, 1 ≤ n,i <∞} be an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 < an ↑∞. The limiting behavior of maximum partial sums 1/an max 1≤k≤n| kΣi=1 Xni| is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].