Authors’ abstract: We analyze a nonlinear two degree-of-freedom model describing a flexible elastic suspended cable undergoing galloping oscillations. By using a perturbative approach, the critical conditions occurring at different values of the aerodynamic coefficient are described. We find two different types of critical conditions, corresponding to simple or to double Hopf bifurcations. The nonlinear postcritical behavior of single taut strings in 1:1 primary internal resonance is studied through the multiple scale perturbation method. In the case of double Hopf bifurcation, we illustrate the influence of detuning between critical eigenvalues on the postcritical behavior. It is found that quasi-periodic motions, which are likely to occur in the linear field when the two critical frequencies are incommensurable, are really unstable in the nonlinear range. Therefore, the postcritical behavior of string consists of stable periodic motions for any detuning values.