Purpose <p>When transmitting power, a gear tooth acts like a cantilever beam under dynamic load, resulting in its flexibility. The flexible deformation of teeth alters the meshing states of spur gear systems (SGS) and induces gear impact, thereby weakening the dynamic performance. This study presents multi-state meshing-impact dynamics of SGS with gear-tooth flexibility (GTF).</p> Methods <p>Two extended corner contact states with GTF are proposed. The tooth-angle relationships are determined based on the engagement states considering GTF. The actual contact ratio and improved time-varying meshing factors (meshing stiffness and load sharing ratio) affected by GTF are modeled and calculated. A multi-state meshing-impact nonlinear dynamic model of SGS considering the meshing factors and GTF is established. The meshing-impact energy dissipation model is developed. The influence of GTF on the dynamic meshing force is examined. The multi-state meshing-impact global nonlinear dynamic characteristics of SGS are studied based on the multi-initial bifurcation diagrams. The mechanism of vibration-impact energy dissipation is revealed under one- and two-parameters spaces. The validity of the results is verified through comparison and discussion.</p> Results <p>The findings indicate that the change of single and double tooth meshing area due to GTF increases the contact ratio. Moreover, time-varying meshing factors change smoothly during the switching of the single- and double-tooth meshes. The GTF reduces the dynamic meshing force during the full drive-side meshing. The multi-initial value bifurcation behavior of SGS considering GTF under parameter changes aggravates the incomplete drive-side meshing, causing meshing-impact energy dissipation.</p> Conclusion <p>The research provides a new approach and theoretical reference for quickly identifying vibration and shock signals.</p>