Abstract: The global asymptotic stability of second order autonomous generalized Birkhoff system is studied by using of Liapunov function method and Кpacoвcий method.Firstly,the form of Liapunov function V of the system is given.Then,the relations between the derivative V of Liapunov function V with respect to time t and the matrix F(a) are verified,and the proposition of global asymptotic stability of the system is proposed.Finally,an example is given to illustrate the application of the result.