Abstract: By introducing the concept of ideal transmission,the expressing way of meshing force and meshing damping is given,which is a foundation to establish complex dynamic equations of spiral bevel gears and hypoid gear drives.Meanwhile,the torque produced by meshing force and meshing damping is given,which is various in different meshing regions under multiple-teeth meshing.The non-linear dynamic equations of spiral bevel gears and hypoid gear drives are established,which include the input and output rotating inertia,transmission error and time-varying mesh stiffness as well as backlash.The frequency response curves,phase portraits,time histories and dynamic load factor can be obtained by calculating the dynamic equations.