To study the non-linear bifurcation characteristics of face-gear transmission system,a nonlinear dynamic model is presented.This model includes bearings,backlash,time-varying meshing stiffness,general transmission error,meshing damping,and external load,etc.The PNF(Poincaré-Newton-Floquet) method is used to solve the dynamic differential equations.The calculation results show: when the amplitude coefficient of time-varying meshing stiffness increases from 0.4 to 0.5,the system will go into chaos through period-doubling bifurcation;when the meshing damping ratio decreases from 0.061 000 0 to 0.060 000 0,the system will enter chaos through quasi-periodicity bifurcation;when non-dimension amplitude of general transmission error decreases from 0.120 to 0.112,the system will appear boundary cataclysm.