The bifurcation analyses of the internal rotation processes of two different series of monorotor molecules along the reduced reaction coordinate are investigated in this Letter. Our topological analyses indicate that the internal rotation processes are characterized by the properties of critical points. Furthermore, when the energy functions are represented as the third-order generic polynomial of the reduced reaction coordinate, the processes are isomorphic to the elementary fold catastrophe. (C) 2003 Elsevier Science B.V. All rights reserved.