The nonlinear hydrodynamic interaction between a floating elliptic cylinder and a vibrating circular cylinder immersed in an infinite fluid was investigated. By taking the added masses of the two-cylinder system into account, the dynamical equations of motion were formulated from the Lagrange equations of motion. The dynamical behaviors of these two cylinders were analyzed numerically for some typical situations, and the results show that the presence of a vibrating circular cylinder has a significant influence on the planar motion of a floating elliptic cylinder. The hydrodynamic interaction between them results in complicated nonlinear behaviors of the floating cylinder. It is found that oscillatory motion of the elliptic cylinder takes place in response to the vibrating mode of the circular one.