  In this short note we show that the closed cone of moving curves of a smooth
Fano-threefold is polyhedral.
  The proof relies on a famous result of Bucksom, Demailly, Paun and Peternell
which says that the strongly movable cone is dual to the cone of
pseudoeffective divisors. Finally, we relate the extremal rays of the cone of
moving curves on a threefold with extremal rays in the cone of strongly movable
curves on a birational model obtained by a Mori contraction.
