The　current　investigation　applied　the　invariant　manifold　technique　to　study　the　halo　orbits　around　the　libration　points　in　circular　restricted　three-body　problem.　Two　dominant　(leading)　directions　were　considered　as　dominant　motions　for　the　construction　of　spatial　halo　orbits,　the　third　direction　motion　being　the　slave　(following)　motion.　The　dominant　motions　correspond　to　four-dimensional　invariant　manifolds　in　the　phase　space.　The　invariant　nonlinear　asymptotic　relations　(i.e.　INARs)　between　the　two　dominant　motions　and　the　slave　motion　were　established,　enabling　a　transformation　from　the　3-DOF　problem　into　a　2-DOF　problem.　Application　of　the　INARs　are　also　discussed.　Such　invariant　nonlinear　relations　in　polynomial　expansion　form　could　be　used　as:　(I)　approximate　analytical　solutions;　(II)　topological　constraints　to　obtain　more　exact　numerical　solutions　with　differential　correction.　General　findings　in　the　current　research　revealed　that　the　nonlinear　asymptotic　relations　among　the　directions　provided　an　alternative　point　of　view　to　explore　the　overall　dynamics　of　halo　orbits　around　libration　points　with　general　rules.　The　effectiveness　of　the　proposed　method　was　also　verified　by　numerical　simulations.