The principal families of periodic orbits that emerge from the stationary points of the six-dimensional potential energy surface bf the C2H2 molecular system, as well as periodic orbits from saddle-node bifurcations, have been located and propagated for an energy range up to 36 500 cm(-1) above the absolute minimum of the potential. The bifurcation diagrams of these periodic orbits reveal the regions of phase space where the dynamics are regular or chaotic (with soft or hard chaos) for acetylene, vinylidene, and the region over these two isomers. An association of the structure of phase space with spectroscopic findings is made by calculating Gutzwiller’s semiclassical trace formula and classical survival probability functions.