Abstract: A definition of the modes of a nonlinear autonomous system was developed. The existence conditions and orbits’ nature of modes are given by using the geometry theory of invariant manifolds that include stable manifold theorem, center maifold theorm and sub-center manifold theorem. The Taylor series exyansion was used inorder to approach the sub-manifolds of the modes and obtain the motions of the mods on the manifolds. Two examples were given to demonstrate the applications.

Key words: invariant manifold, mode, nonlinear system