  Berry phase, which had been discovered for more than two decades, provides us
a very deep insight on the geometric structure of quantum mechanics. Its
classical counterpart--Hannay's angle is defined if closed curves of action
variables return to the same curves in phase space after a time evolution. In
this paper, we study the Berry phase and Hannay's angle in a quantum-classical
hybrid system under the Born-Oppenheimer approximation. By quantum-classical
hybrid system, we denote a composite system consists of a quantum subsystem and
a classical subsystem. The effects of subsystem-subsystem couplings on the
Berry phase and Hannay's angle are explored. The results show that the Berry
phase has been changed sharply by the couplings, whereas the couplings have
small effect on the Hannay's angle.
