This study deals with the coupled lateral-torsional vibration of a two-stage gear train system. First the equations of motion are derived, which have periodically varying parameter, and the solutions of equations are obtained analytically and characteristics of the vibration of the system are analyzed. The response to the forced vibration under static load is analyzed and some new results are obtained. Some resonances of dynamic tooth load appeared when the meshing frequency equals to fractional natural frequency. In some cases the phase angle between two meshing stiffneses influence the amplitude of dynamic tooth load. Tooth contact ratio also influences the amplitude of dynamic tooth load. By considering these results it is known that some resonances of the system can be avoid by adopting an adequate phase or contact ratio.