  Let $\mathcal{H}$ be a hypergraph of maximal vertex degree $\Delta$, such
that each its hyperedge contains at least $\delta$ vertices. Let
$k=\lceil\frac{2\Delta}{\delta}\rceil$. We prove that (i) The hypergraph
$\mathcal{H}$ admits proper vertex coloring in $k+1$ colors. (ii) The
hypergraph $\mathcal{H}$ admits proper vertex coloring in $k$ colors, if
$\delta\ge 3$ and $k\ge 3$. As a consequence of these results we derive upper
bounds on the number of colors in dynamic colorings.
