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In this paper we survey on some recent results on Riemannian orbifolds andsingular Riemannian foliations and combine them to conclude the existence ofclosed geodesics in the leaf space of some classes of singular Riemannianfoliations (s.r.f.), namely s.r.f. that admit sections or have no horizontalconjugate points. We also investigate the shortening process with respect toRiemannian foliations.

On closed geodesics in the leaf spaces of singular Riemannian foliations