Abstract: The dynamical character for a perturbed coupled nonlinear Schrödinger system with periodic boundary condition was studied.First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.

Key words: coupled nonlinear Schrö, dinger system, dynamical character, invariant manifold