  We consider a linear Schr\"odinger equation with a small nonlinear
perturbation in $R^3$. Assume that the linear Hamiltonian has exactly two bound
states and its eigenvalues satisfy some resonance condition. We prove that if
the initial data is near a nonlinear ground state, then the solution approaches
to certain nonlinear ground state as the time tends to infinity. Furthermore,
the difference between the wave function solving the nonlinear Schr\"odinger
equation and its asymptotic profile can have two different types of decay: 1.
The resonance dominated solutions decay as $t^{-1/2}$. 2. The radiation
dominated solutions decay at least like $t^{-3/2}$.
