  We prove that a $C^2$ diffeomorphism $f$ of a compact manifold $M$ satisfies
Axiom A and the strong transversality condition if and only if it is H\"{o}lder
stable, that is, any $C^1$ diffeomorphism $g$ of $M$ sufficiently $C^1$ close
to $f$ is conjugate to $f$ by a homeomorphism which is H\"{o}lder on the whole
manifold.
