A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper. Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity in-fluence such as time-varying mesh stiffness, backlash and dynamic transmission error (DTE) were obtained. The method of multiple scales was employed to solve the nonlinear differential equations with parametric excita-tion in gear systems, by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained. The nonlinear influence of stiffness variation, the damping and the internal excitation on the system response was shown by fre-quency-response curves. Compared with numerical examples, the approximate analytical solutions are in good a-greement with exact solutions, which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.