Abstarct: Galloping of cables is a kind of self-excited vibration with high amplitude and low frequency. In this thesis, baxsed on the curved-beam theory, a nonlinear galloping model considering four degrees of freedom (normal, bi-normal and tangential displacement components and twist), bending stiffness and torsional stiffness, for a horizontal iced cable with eccentricity of cross section, in two cases simply support cable and elastically constrained on a cable support (normal and bi-normal directions), is formulated. Aerodynamic modeling is also done with the assumption of quasi-steady theory. The equations of motion include four equations, using a reduced galloping model, the number of equations has reached two. These two equations that contain quadratic and cubic nonlinearities in both velocity and displacement terms, are discretized via the Galerkin method. By using Multiple Scale method, for simply support cable in two cases 1:1 and 2:1 internal resonant and for elastically constrained on a cable support in five cases 1:1, 2:1, 3:1, 1:2 internal resonant and no internal resonant, Reduced Amplitude Modulation Equations (RAME) is obtained. The RAME equations are solved and the results are presented for different states of the stiffness of the support in two directions, normal and bi-normal. Finally, to ensure the accuracy of the results, two equations of the reduced model are solved by numerical simulation and the results proved by the reduced model numerically integrated in time history. Wind speed, stiffness of the support in two directions (normal and bi-normal) and time are as variable parameters in the results.