The stability problem of equilibrium for a generalized Birkhoffian system is studied. The equations of equilibrium for the autonomous generalized Birkhoffian system are established. The equations of first approximation of the system are given, and the criterion of stability for equilibrium state of the system is established by using the Liapunovs first approximation theory. The Liapunovs function is constructed, and the criterion of stability for equilibrium state of the system is established by using the Liapunovs direct method. Some examples are given to illustrate the application of the results.