Due to the influence of load, the flexible characteristic of gear teeth during meshing leads to a deviation of meshing position from the theoretical meshing line, thereby affecting engagement and system’s dynamic response. Building upon a profound comprehension of the meshing theory and dynamic response of the spur gear system (SGS), this study identifies the precise location of the meshing point considering gear teeth flexibility (GTF) and computes the actual contact ratio along with an analytical model for the time-varying meshing stiffness. A nonlinear dynamic model of the SGS system is developed, incorporating meshing factors and GTF to account for multi-state meshing behavior. The global nonlinear dynamics under varying meshing conditions are analyzed using multi-initial bifurcation diagrams. Key results indicate that GTF enhances the contact ratio. Additionally, the time-varying meshing stiffness exhibits gradual transitions when shifting between different meshing states. Parameter variations induce multi-initial bifurcation in the GTF-influenced SGS system, exacerbating incomplete meshing on the drive side.