The costs of design and construction of long-span bridges have currently increased significantly under the guidance of linear flutter theory, which has seriously hindered the further development of long-span bridges. Therefore, it is urgent to investigate the characteristics of nonlinear flutter of long-span bridges and establish corresponding analytical methods or theories of nonlinear bridge flutter. This will help provide theoretical basis for the establishment of more economical design specifications that can fully utilize the safety margin at post-critical regime. In this study, a method for identifying amplitude-dependent flutter derivatives based on free vibration wind tunnel tests is proposed, and multimode/full-mode analysis methods and a time-domain analysis method for three-dimensional nonlinear coupled flutter are established. Meanwhile, the section model wind tunnel testing technique that investigates the nonlinear bridge flutter with large amplitudes is developed. Then, based on the developed nonlinear flutter analysis methods, a typical long-span double-deck truss suspension bridge with four main cables is used as a case study. The characteristics of the nonlinear flutter for this typical double-deck truss section of the bridge is investigated by section model tests with large vibration amplitudes; the impact of the vertical degree of freedom on the nonlinear flutter of the double-deck section is quantified and discussed; the influence of multimode aerodynamic coupling effects on the 3D nonlinear flutter of the bridge is investigated; the super-harmonic resonance behavior induced by the geometric nonlinear effects is observed in the nonlinear bridge flutter and the mechanism of the influence of the geometric nonlinear effects on the nonlinear bridge flutter is revealed based on the observations. As a result, readers may have a relatively more comprehensive understanding of the nonlinear flutter theory and analysis methods. Besides, the results of this study can provide theoretical and technical supports for the establishment of more economical wind design specifications for resilient large-span bridges in the future.