Abstract: The discrete nonlinear governing equations for stay cables are derived by using the Galerkin method to ascertain the effects of longitudinal floating vibrations of a girder on the nonlinear dynamic responses of its stay cables. Matlab and DSolver are employed to solve the ordinary differential equations and well-agreed results are found. Nonlinear responses under two excitation amplitudes are investigated by amplitude-response maps for the cases of a consolidated system, small longitudinal vibrations and large longitudinal vibrations. The results indicate that longitudinal floating of a girder is efficient to ease large amplitude responses of its stay cables, but it should be reasonably set. The invariant responses of cables would engage if both the sums of axial (parametric excitation) and transverse (forced excitation) components of excitations are not change.