In this paper, chromatic polynomials of (non-uniform) hypercycles, unicyclic hypergraphs, hypercacti and sunflower hypergraphs are presented. The formulae generalize known results for $r$-uniform hypergraphs due to Allagan, Borowiecki/Łazuka, Dohmen and Tomescu. Furthermore, it is shown that the class of (non-uniform) hypertrees with $m$ edges, where $m_r$ edges have size $r$, $r\geq 2$, is chromatically closed if and only if $m\leq4$, $m_2\geq m-1$.

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