  Given a smooth non-hyperelliptic prime Fano threefold X, we prove the
existence of all rank 2 ACM vector bundles on X by deformation of semistable
sheaves. We show that these bundles move in generically smooth components of
the corresponding moduli space. We give applications to pfaffian
representations of quartic threefolds in P^4 and cubic hypersurfaces of a
smooth quadric of P^5.
