Abstract: The definition of the nonlinear normal modes is given by introducing the undivided even dimensional invariant manifold, and a new kind of normal modes (i.e. coupled nonlinear mode) are proposed which may classify all the normal modes expected in physical systems. This idea of classification may form a new base of constructing the nonlinear normal mode theory. Modal oscillators obtained by the method presented here are of Normal Form type,which are simplest in expression and can represent the main dynamical...