Abstract: In this paper, taking the sagging effect and geometrical non-linearity into consideration, the nonlinear equations of stay cables for coupling in-plane and out-of-plane vibrations are derived. By the Galerkin method, the partial differential equations are transformed into ordinary differential equations, which are solved with multi-scale method. The nonlinear modal interaction characteristics of cables of cable-stayed bridges are obtained. Some typical cables of cable-stayed bridges are investigated. The results demonstrate that 1:1 internal resonance may occur and both the resonance frequency range and the response amplitude are related with the initial sag of cable. And cable damping affects the internal resonance significantly. Also, the response amplitude is changed with the initial conditions due to the nonlinear effects of the cables.