Libration　points　are　the　five　equilibrium　solutions　in　the　circular　restricted　three　body　problem　(i.e.　CRTBP),　including　three　collinear　points　and　two　triangular　libration　points.　Studies　about　probes　moving　around　orbits　in　the　vicinity　of　the　libration　points　have　theoretical　significance.　In　this　study,　we　extend　the　method　proposed　by　Qian　and　Yang　(Astrophys　Space　Sci　362(8):136,2017),　(Nonlinear　Dyn　91(1):39-54,2018).　Two　dominant　motions　are　considered　for　the　construction　of　spatial　halo　orbits.　Based　on　the　invariant　manifold　theory,　the　xi　and　zeta-component　motions　are　selected　as　the　dominant　motions　for　halo　orbits,　eta-component　motion　as　slave　motion.　The　invariant　nonlinear　asymptotic　relations　between　the　two　dominant　motions　and　the　slave　motion　are　obtained.　By　employing　the　relations　among　the　three　directions,　the　three-dimensional　system　can　be　transferred　into　a　two-dimensional　problem.　As　one　of　the　applications,　the　invariant　nonlinear　relations　in　polynomial　expansion　form　are　used　as　constraints　to　obtain　numerical　solutions　by　differential　correction.　The　nonlinear　asymptotic-relations　among　the　directions　provide　an　alternative　point　of　view　to　explore　the　overall　dynamics　of　periodic　orbits　around　libration　points　with　general　rules.　Numerical　simulations　verify　the　efficiency　of　the　proposed　method.