Abstract: In this paper the asymptotic stability of the partially damped linear mechanical system with gyroscopic forces is studied. The equation of motion for the system is a second order linear matrix differential equation. The stiffness matrix is assumed to be positive definite representing the conservative forces and then Lyapunov's second method is employed. By splitting the system matrices in block matrices the condition of asymptotic stability （e. g, the condition of pervasiveness） can be expressed as a rank condition of certain matrix with dimension lower than that of the system. Several cases with different gyroscopic coupling are discussed. The stability condition is not only simpler than that obtained by former authors, but also gives some insight to the mechanical properties of the system since it may be considered as two coupled subsystems then.