By introducing frequency dependent unsteady self-excited forces in terms of rational functions, the equations of bridge motion are expressed in a frequency independent state-space format. It is applied to the coupled multi-mode flutter analysis of long span bridges through the solution of a linear complex eigenvalue problem. The contribution of aerodynamic coupling among modes and the contribution of each self-excited force component along the bridge axis to the system damping are identified. The coupling effects on the buffeting response are also discussed.