A definition of the modes of a nonlinear autonomous system was developed. T
he 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
expansion was used in order 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.