  The famous Dirac's Theorem gives an exact bound on the minimum degree of an
$n$-vertex graph guaranteeing the existence of a hamiltonian cycle. We prove
exact bounds of similar type for hamiltonian Berge cycles in $r$-uniform,
$n$-vertex hypergraphs for all $3\leq r< n$. The bounds are different for
$r<n/2$ and $r\geq n/2$. We also give bounds on the minimum degree guaranteeing
existence of Berge cycles of length at least $k$ in such hypergraphs; the
bounds are exact for all $k\geq n/2$.
