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. (C) 2003 Elsevier B.V. All rights reserved.