Abstract: The health management concept was burgeoned as the application of engineering system. Several basic formulation definitions, such as health vector, health index, health function, were presented to mitigate the lack of formal concepts for the system health. Compared with the traditional condition parameters based component health description method, the engineering system level health condition can be effectively represented and the dynamic essence of health decrease can be revealed by using the health formulation definitions. Employing the Volterra series system description approach and analyzing the system through generalized frequency response function(GFRF), the system health vector was constructed based on the concepts of engineering system health, and the health of a kind of nonlinear system was monitored by the GFRF method. The nonlinear spring-mass-dashpot system was used as the research object. The relation between system health monitoring data and health index was given through simulation. And the simulated data show that the system health formulation definitions are effective and the system health monitoring approach based on GFRF is feasible.