An approach for classifying and organizing spectra of highly excited vibrational states of molecules is investigated. As a specific example, we analyze the spectrum of an effective spectroscopic fitting Hamiltonian for H2O. In highly excited spectra, multiple resonance couplings and anharmonicity interact to give branching of the N original normal modes into new anharmonic modes, accompanied by the onset of widespread chaos. The anharmonic modes are identified by means of a bifurcation analysis of the spectroscopic Hamiltonian. A diabatic correlation diagram technique is developed to assign the levels with approximate "dynamical" quantum numbers corresponding to the dynamics determined from the bifurcation analysis. The resulting assignment shows significant disturbance from the conventional spectral pattern organization into sequences and progressions. The "dynamical" assignment is then converted into an assignment in terms of "nominal" quantum numbers that function like the N normal mode quantum numbers at low energy. The nominal assignments are used to reconstruct, as much as possible, an organization of the spectrum resembling the usual separation into sequences and progressions.