A generalized skewgradient system is proposed, and the generalized skewgradient representation for a Birkhoff system is studied. A condition under which the Birkhoff system can be considered as a generalized skewgradient system is obtained. The characteristic of generalized skewgradient system is then used to study the stability of the Birkhoff system. The application of this developed generalized skewgradient system is also presented through some case studies in this paper.