  We study the existence of closed geodesics on compact Riemannian orbifolds,
and on noncompact Riemannian manifolds in the presence of a cocompact,
isometric group action. We show that every noncontractible Riemannian manifold
which admits such an action, and every odd-dimensional, compact Riemannian
orbifold has a nontrivial closed geodesic.
