  We consider a nonlinear Schr\"odinger equation in $\R^3$ with a bounded local
potential. The linear Hamiltonian is assumed to have two bound states with the
eigenvalues satisfying some resonance condition. Suppose that the initial data
is small and is near some nonlinear {\it excited} state. We give a sufficient
condition on the initial data so that the solution to the nonlinear
Schr\"odinger equation approaches to certain nonlinear {\it ground} state as
the time tends to infinity.
