  In this note we extend to non trivial Hamiltonian fibrations over
symplectically uniruled manifolds a result of Lu's, \cite{Lu}, stating that any
trivial symplectic product of two closed symplectic manifolds with one of them
being symplectically uniruled verifies the Weinstein Conjecture for closed
separating hypersurfaces of contact type, under certain technical conditions.
The proof is based on the product formula for Gromov-Witten invariants
($GW$-invariant) of Hamiltonian fibrations derived in \cite{H}.
