The galloping vibrations of a single transmission cable that may vibrate transversely and torsionally has been investigated via a two-degree-of-freedom oscillator. The analytical solutions of periodic motions for this two-degree-of-freedom system are represented by the finite Fourier series. The analytical bifurcation trees of periodic motions to chaos of a transmission line under both steady and unsteady flows are discussed from the generalized harmonic balance method. The analytical solutions for stable and unstable periodic motions in such a two degree-of-freedom system are achieved, and the corresponding stability and bifurcation was discussed. The limit cycle for the linear cable structure are obtained by gradually decreasing the sinusoidal excitation amplitude. In addition, the numerical simulations of stable and unstable periodic motions are illustrated. The rich dynamical behavior in such a nonlinear cable structure are discovered, and this investigation may help one better understand the galloping phenomena for any elastic structures.