Let $X_1,X_2,cdots$ be identically distributed $ ho$-mixing random variables with mean zeros and positive finite variances. In this paper, we prove $$array{lim\{in}downarrow0}{in}^2 sumlimits_{n=3}^inftyfrac{1}{nlogn}P({mid}S_nmidgeqinsqrt{nloglogn}=1$$, $$array{lim\{in}downarrow0}{in}^2 sumlimits_{n=3}^inftyfrac{1}{nlogn}P(M_ngeqinsqrt{nloglogn}=2 sumlimits_{k=0}^inftyfrac{(-1)^k}{(2k+1)^2}$$ where $S_n=X_1+cdots+X_n,;M_n=max_{1{leq}k{leq}n}{mid}S_k{mid}$ and $sigma^2=EX_1^2+ 2sumlimits{^{infty}_{i=2}}E(X_1,X_i)=1$.