  Dirac proved that each $n$-vertex $2$-connected graph with minimum degree $k$
contains a cycle of length at least $\min\{2k, n\}$. We obtain analogous
results for Berge cycles in hypergraphs. Recently, the authors proved an exact
lower bound on the minimum degree ensuring a Berge cycle of length at least
$\min\{2k, n\}$ in $n$-vertex $r$-uniform $2$-connected hypergraphs when $k
\geq r+2$. In this paper we address the case $k \leq r+1$ in which the bounds
have a different behavior. We prove that each $n$-vertex $r$-uniform
$2$-connected hypergraph $H$ with minimum degree $k$ contains a Berge cycle of
length at least $\min\{2k,n,|E(H)|\}$. If $|E(H)|\geq n$, this bound coincides
with the bound of the Dirac's Theorem for 2-connected graphs.
