  We notice that, when a quantum system involves exceptional points, i.e. the
special values of parameters where the Hamiltonian loses its self-adjointness
and acquires the Jordan block structure, the corresponding classical system
also exhibits a singular behaviour associated with restructuring of classical
trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2
-igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies
with supersymmetric Yang-Mills dynamics are elucidated.
