Abstract Nonlinear effects in rotational spectra of molecules and atomic nuclei caused by a centrifugal distortion for high values of an angular momentum quantum number J are investigated. The theoretical analysis is based on a new expansion form of the effective rotational Hamiltonian. It is shown that qualitative changes of rotational motion may occur in the rotational spectra for some value J c of the quantum number J. These phenomena which are in some sense analogous to the macroscopic phase transitions are called critical phenomena and correspond to bifurcations in classical mechanics. The classification of critical phenomena for a purely rotational motion is given. This classification is based on the concept of a local symmetry group G . There exist five types of critical phenomena in the rotational spectra. The local critical phenomena occuring in a bounded region of the rotational motion phase space are specially discussed. In the classical limit the local critical phenomena are characterized by a broken symmetry G and discontinuity of the second derivative of the rotational energy with respect to J at J c. A universal rotational Hamiltonian is shown to exist in the neighborhood of J c, which does not depend on the dynamical systems internal structure up to numerical values of its parameters. A phenomenological theory of the local critical phenomena is developed with the aid of universal Hamiltonians. The difference between the local critical phenomena and second-order phase transitions in macroscopic systems is shown.