The limit cycle oscillations (LCOs) exhibited by long-span suspension bridges in post-flutter condition are investigated. A parametric dynamic model of prestressed long-span suspension bridges is coupled with a nonlinear quasi-steady aerodynamic formulation to obtain the governing aeroelastic partial differential equations adopted herewith. By employing the Faedo–Galerkin method, the aeroelastic nonlinear equations are reduced to their state-space ordinary differential form. Convergence analysis for the reduction process is first carried out and time-domain simulations are performed to investigate LCOs while continuation tools are employed to path follow the post-critical LCOs. A supercritical Hopf bifurcation behavior, confirmed by a stable LCO, is found past the critical flutter condition. The analysis shows that the LCO amplitude increases with the wind speed up to a secondary critical speed where it terminates with a fold bifurcation. The stability of the LCOs within the range bracketed by the Hopf and fold bifurcations is evaluated by performing parametric analyses regarding the main design parameters that can be affected by uncertainties, primarily the structural damping and the initial wind angle of attack.