  We prove Wadsley's theorem for foliations by closed non-lightlike geodesics.
As an application we show that every pseudo-Riemannian and non-Riemannian
2-mainfold, all of whose time- or spacelike geodesics are closed, is
diffeomorphic to $S^1\times \R$. Further we show that every pseudo-Riemannian
2-manifold with index 1 contains a non-closed timelike or spacelike geodesic.
