With the rapid development of the long-span bridges, modern bridges are becoming more and more sensitive to wind action. The conventional wind resistance measure and design method can not fulfill the construction and design requirement. It is necessary to further adopt some aerodynamic measure or mechanical measure to reduce the wind-induced vibration response of long span bridges. And the most important theoretical and technical part of those measures is a combination of multimode coupled flutter and buffeting analysis and the conventional passive control theory. The conventional buffeting control theory is in accordance with single-mode-based (SRSS) method which can not account for the effects of aerodynamic coupling among the modes. The conventional flutter control theory is based on the classical coupled flutter analytical method. In this method, the effects of multimode participation can not be considered. Currently, multimode coupled flutter and buffeting analytical method is developed and widely used to determinate the flutter and buffeting response of long-span bridges to wind excitation. Therefore, to develop multimode coupled flutter and buffeting control method to take into account the effects of multimode participation and aerodynamic coupling among the modes is of great theoretical and practical value.Based on multimode coupled flutter and buffeting theory proposed by Scanlan and passive control theory, a most comprehensive method for multimode coupled flutter and buffeting control using various passive control devices for bridges is established in this thesis. In this method, multimode participation and aerodynamic coupling among the modes as well as among the modal displacement components in a mode are all taken into account in the formulation and each control device can be installed anywhere on the bridge deck. Finally, numerical examples of the Yamen cable-stayed bridge and the Hong Kong TingKao Bridge are presented to investigate the effectiveness and robustness of various control devices. Such control devices include tuned mass damper(TMD), multiple tuned mass dampers(MTMD), tuned mass damper with dual frequencies(DTMD) and multiple DTMDs. The objective is to increase the critical flutter velocity and to reduce the buffeting response. Since the proposed method is based on multimode coupled flutter and buffeting analysis, the optimum parameters of the control devices obtained from the proposed method are