The Invariant Manifold Structure of the Spatial Hill's Problem G. Gomez, M. Marcote and J.M. Mondelo Abstract. The paper studies the invariant manifolds of the spatial Hill's problem associated to the two liberation points. A combination of analytical and numerical tools allow the normalization of the Hamiltonian and the computation of periodic and quasi-periodic (invariant tori) orbits. With these tools, it is possible to give a complete description of the center manifolds, association to the liberation points, for a large set of energy values. A systematic exploration of the homoclinic and heteroclinic connections between the center manifolds of the liberation points is also given.