M. Joyeux, D. A. Sadovskii, and J. Tennyson Using the potential surface of Essers, Tennyson, and Wormer in [Chem. Phys. Lett. 89 (1982) 223] we show that the system of bending vibrational states of the isomerizing molecule LiNC/NCLi has monodromy. On the basis of a deformed spherical pendulum model we explain dynamical and geometric reasons of this phenomenon and of its absence in the similar system HCN/CNH. PACS: 33.20.Vq; 45.50.-j; 03.65.Sq; 33.15.Mt Keywords: Floppy triatomic molecules; Global quantum numbers; Monodromy; Energy-momentum map submitted to Chem. Phys. Lett. 9/2003