To study the influence of the tooth surface contact fatigue on the safety characteristics of gear systems， its safety condition of the spur gear transmission system is established based on the Hertz contact theory. The multi-state meshing including single pair teeth meshing， double pair teeth meshing， tooth disengagement and back- side contacting are considered. Attracting domains of the system and their evolutions with the change of control parameters are numerically calculated by the cell-to-cell method in the investigation region. The safety characteristics of coexistence attracting domains in the region are analyzed under the established safety condition. Safe basins and their evolutions process in the region are analyzed. The erosion and bifurcation mechanism of safe basins for the system are studied according to multi-initial bifurcation diagrams and top Lyapunov exponent diagrams. Results show that the safety characteristics of coexistence attraction domains in the survey area are different under the tooth surface contact safety condition. The disappearance or appearance of attractors is the main cause of the bifurcation for safe basins and their instability. Bifurcation of the safe basin is caused by the periodic jumping or bifurcation. Results can provide references for parameter selection or failure prediction of the gear transmission system.