Fazekas and Klesov[Fazekas.I.,Klesov,O.,2000.A general approach to the strong law of large numbers.Theory of Probability and its Applications 45,436-449]established a Hajek-Renyi-type maximal inequality and obtained a strong law of large numbers(SLLN)for the sums of random variables.Hu and Hu[Hu Shuhe,Hu Ming,2006.A general approach rate to the strong law of large numbers.Statistics and Probability Letters 76,843-851] obtained the SLLN and the growth rate for a sequence of random variables by using the Hajek-Renyi-type maximal inequality.This paper obtains some new results of the SLLN and growth rate for strongly positive dependent stochastic sequences,PA sequences,(rho)over bar-mixing sequences,(phi)over bar-mixing sequences and pairwise negatively quadrant dependent sequences
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