  Let $(M,g)$ be a $C^{\infty}$ compact, boudaryless connected manifold without
conjugate points with quasi-convex universal covering and divergent geodesic
rays. We show that the geodesic flow of $(M,g)$ is $C^{2}$-structurally stable
from Ma\~{n}\'{e}'s viewpoint if and only if it is an Anosov flow, proving the
so-called $C^{1}$-stability conjecture.
