The bending dynamics of acetylene are analyzed starting from spectroscopic fitting Hamiltonians used to fit experimental spectra. The possibility is considered of a transformation in the dynamics from normal to local bending modes, as well as a new kind of correlated bending motion called precessional modes. The spectroscopic fitting Hamiltonian of C2H2 is discussed with particular attention to the coupling interactions present due to Fermi and Darling-Dennison resonances. It is argued that for analysis of experiments in which the energy is initially placed in the bends,:many couplings can be neglected. Of the remaining couplings, that responsible for the primary pathway of energy transfer out of the bends is a single Darling-Dennison coupling between the bends. A Hamiltonian containing this coupling alone is analyzed to isolate the bending dynamics involved in the primary energy transfer pathway. The anharmonic modes born in bifurcations from the low-energy normal modes are determined from analysis of the classical form of the Hamiltonian. In addition to the usual normal modes, local and precessional modes are found. Precessional modes have relative phases of pi/2 or 3 pi/2, with one local bend fully extended while the other has maximal velocity. Sets of levels or "polyads" with the same total number of bend quanta are plotted in phase space on the polyad phase sphere, allowing a determination of the normal, local, or precessional character of a given quantum state. It is determined that local modes are found in the experimentally observed bend polyads with P greater than or equal to 14, and precessional modes are found in the, polyads P greater than or equal to 20. Polyads are classified on the molecular catastrophe map according to their structure of normal, local, and precessional modes. Energy level spacing patterns within a polyad, shown previously to be characteristic of phase space bifurcation structure, are determined and correlated with the phase sphere. A diabatic correlation diagram analysis, previously applied to H2O, is suggested to extend the analysis here of normal, local, and precessional bending states to the full multiresonance, chaotic spectral fitting Hamiltonian.