Abstract: Conventional dynamic models for geared systems typically simplify tooth contact as a normal impact, ignoring the oblique collision that involves coupling between normal extrusion and tangential sliding when teeth transition from disengagement to meshing. To remedy this deficiency, this study establishes an oblique collision dynamics model based on Hertzian contact theory and fractal contact theory, accounting for normal extrusion and tangential slip deformations. This model is then incorporated into a three-state meshing framework that comprises tooth surface meshing, disengagement, and back-side contact, ultimately constructing a multi-state meshing-oblique collision dynamic model for gear systems. The dynamic mechanism of normal and tangential deformations during oblique collision is analyzed using phase diagrams and time-history plots, and the distribution characteristics of maximum energy dissipation under two-parameter correlation are studied. Moreover, by employing multi-initial bifurcation diagrams, bifurcation trees, and basins of attraction, the global bifurcation evolution of the meshing-oblique-collision behavior is revealed. The results indicate that normal deformation is consistently larger than tangential deformation, and the abrupt variation leads to non-smooth phase trajectories. Notably, the restitution coefficient exhibits periodic variations with motion type, rather than remaining constant as in traditional models. Under multi-initial conditions, incomplete bifurcation is identified as the cause of multi-stability coexistence, which leads to simultaneous presence of multiple bifurcation branches and steady-state responses. Experimental comparisons show that the model considering oblique collisions in this paper achieves significantly higher accuracy than traditional models. This study provides a new theoretical basis for vibration suppression in high-precision gear transmissions.