The stabilities of the equilibrium state in relativistic Birkhoff autonomous systems, relativistic Birkhoff semiautonomous systems and relativistic Birkhoff nonautonomous systems are studied .The equilibrium state equations are given. The disturbance equation and the first approximate equation are established. The stability criteria for the equilibrium state are obtained. The relationship between the stabilities of the equilibrium state in relativistic Birkhoff systems and classical Birkhoff systems is discussed. Several examples are presented to illustrate the results.