  When a magnetic ion vibrates in a metal, it inevitably introduces a new
channel of hybridization with conduction electrons and in general, the
vibrating ion induces electric dipole moment. In such a situation, we find that
magnetic and non-magnetic Kondo effects alternatively occur due to the
screening of spin moment and electric dipole moment of vibrating ion. In
particular, electric dipolar two-channel Kondo effect is found to occur for
weak Coulomb interaction. We also show that magnetically robust heavy-electron
state appears near the fixed point of electric dipolar two-channel Kondo
effect. We believe that the {\it vibrating} magnetic ion opens a new door in
the Kondo physics.
