A classical phase space analysis is performed for the stretch vibrations of H2O and SO2 by taking the classical limit of the algebraically expanded effective Hamiltonian. It is demonstrated that the Hamiltonian surface specified by a multiplet quantum number, represented by two intrinsic phase-space variables, is useful in characterizing the transition from a normal mode to a local mode. From the classical trajectories on the Hamiltonian surfaces, the onset of the normal-to-local transition in the highly excited SO2 is clearly identified, which could not appear directly in the nodal patters of the vibrational wave functions.