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A state-space method is proposed to analyze the aerodynamically coupled flutter problems oflong-span bridges based on the modal coordinates of structure. The theory about complex modes isapplied in this paper. The general governing equation of the system is converted into a complex standardcharacteristic equation in a state space format, which contains only two variables. The proposed method isa single-parameter searching method about reduced velocity, and it need not choose the participatingmodes beforehand and has no requirement for the form of structure damping matrix. The informationabout variations of system characteristics with reduced velocity and wind velocity can be provided. Themethod is able to find automatically the lowest critical flutter velocity and give relative amplitudes, phasesand energy ratios of the participating modes in the flutter motion. Moreover, the flutter analysis ofJiangyin Yangtse suspension bridge with 1385 m main span is performed. The proposed method hasproved reliable in its methodology and efficient in its use.