  Dirac proved that each $n$-vertex $2$-connected graph with minimum degree at
least $k$ contains a cycle of length at least $\min\{2k, n\}$. We consider a
hypergraph version of this result. A Berge cycle in a hypergraph is an
alternating sequence of distinct vertices and edges $v_1,e_2,v_2, \ldots, e_c,
v_1$ such that $\{v_i,v_{i+1}\} \subseteq e_i$ for all $i$ (with indices taken
modulo $c$). We prove that for $n \geq k \geq r+2 \geq 5$, every $2$-connected
$r$-uniform $n$-vertex hypergraph with minimum degree at least ${k-1 \choose
r-1} + 1$ has a Berge cycle of length at least $\min\{2k, n\}$. The bound is
exact for all $k\geq r+2\geq 5$.
