Summary: ``A {\it star coloring} of a graph $G$ is a proper vertex coloring of $G$ such that any path of length 3 in $G$ is not bicolored. The {\it star chromatic number} $\chi_s(G)$ of $G$ is the smallest integer $k$ for which $G$ admits a star coloring with $k$ colors. A {\it acyclic coloring} of $G$ is a proper coloring of $G$ such that any cycle in $G$ is not bicolored. The {\it acyclic chromatic number} of $G$, denoted by $a(G)$, is the minimum number of colors needed to acyclically color $G$. In this paper, we present upper bound for the star and acyclic chromatic numbers of the generalized lexicographic product $G[h_n]$ of graph $G$ and disjoint graph sequence $h_n$, where $G$ exists a $k$-colorful neighbor star coloring or $k$-colorful neighbor acyclic coloring. In addition, the upper bounds are tight.''