Semiclassical techniques are used to analyze highly excited pure bending vibrational dynamics from spectra of C2H2. An analytic bifurcation approach is developed, based on critical points of a classical version of the quantum fitting Hamiltonian. At high energy four new types of anharmonic modes are born in bifurcations of the normal modes: local, orthogonal, precessional, and counter-rotator. Visual insight into their nature is obtained with the help of computer-generated three-dimensional animations. The connection between the local mode and the acetylene-vinylidene isomerization "reaction mode" is considered.