  The Tur\'an number of a $k$-uniform hypergraph $H$, denoted by
$e{x_k}\left({n;H} \right)$, is the maximum number of edges in any $k$-uniform
hypergraph $F$ on $n$ vertices which does not contain $H$ as a subgraph. Let
$\mathcal{C}_{\ell}^{\left(k \right)}$ denote the family of all $k$-uniform
minimal cycles of length $\ell$, $\mathcal{S}(\ell_1,\ldots,\ell_r)$ denote the
family of hypergraphs consisting of unions of $r$ vertex disjoint minimal
cycles of length $\ell_1,\ldots,\ell_r$, respectively, and
$\mathbb{C}_{\ell}^{\left(k \right)}$ denote a $k$-uniform linear cycle of
length $\ell$. We determine precisely
$e{x_k}\left({n;\mathcal{S}(\ell_1,\ldots,\ell_r)} \right)$ and
$e{x_k}\left({n;\mathbb{C}_{{\ell_1}}^{\left(k \right)}, \ldots,
\mathbb{C}_{{\ell_r}}^{\left(k \right)}} \right)$ for sufficiently large $n$.
The results extend recent results of F\"{u}redi and Jiang who determined the
Tur\'an numbers for single $k$-uniform minimal cycles and linear cycles.
