In this paper we use the concept of $k$-domination, where $k\geq 1$. We determine minimum $k$-dominating sets and $k$-domination numbers of three special types of hexagonal cactus chains. Those are para-, meta- and ortho-chains. For an arbitrary hexagonal chain $G_h$ of length $h\geq 1$ we establish the lower and the upper bound for $k$-domination number $\gamma_k$. As a consequence, we find the extremal chains due to $\gamma_k$.