**B. Zhilinskii**

Classical Hamiltonian monodromy characterises integrable Hamiltonian dynamical systems which possess local action-angle variable but do not have global ones. Corresponding quantum systems appear naturally in many model molecular problems. During last years a significant progress was achieved in understanding and describing the characteristic patterns of systems of common eigenvalues of mutually commuting operators in the case of nontrivial quantum monodromy, i.e. in the case of presence of the obstruction to the existence of global quantum numbers for integrable approximations. The description of quantum monodromy is related with the presence of specific defects in the lattice of quantum states. Concrete molecular examples showing the presence of quantum monodromy, such as CO2 molecule, general problem of angular momenta recouplings, etc. will be used to explain the notion of quantum monodromy and its relation to assignement problem.