Abstract: Let $\{\xi_n,n\geq 1\}$ be a sequence of positive random variables with $\ep \xi_1=\theta>0$, and $S_n=\sum\limits^n_{n=1}\xi_i, Y_n=n\theta\log (S_n/(n\theta))$. In this article, the author gives strong approximations of power sums $\{Y_n\}$ be Wiener
process when $\{\xi_n\}$ is a sequence of independent identically disributed random variables or a sequence of $\varphi$-mixing stationary random variables.

Key words: Power sums, Strong approximation, Wiener process