Contreras G., Iturriaga R., Sanchez-Morgado H. On the creation of conjugate points for Hamiltonian systems. (24K, LATeX 2e) ABSTRACT. We consider a convex Hamiltonian H on the cotangent bundle of a compact manifold M and a fixed energy level e. We prove that the set of potentials f such that H+f defines an Anosov flow is the interior of the set of potentials f such that the flow defined by H+f has no points.