A micro piezoelectric precision drive system is proposed, which is advantageous due its small size, large transmission ratio, and large output torque. The working principle of the proposed piezoelectric precision drive system is presented, and the nonlinear dynamic model and equations of the system are established. Using the Linz Ted-Poincaré and perturbation methods, the nonlinear approximate solutions of the dynamic equations are calculated. The results indicate that the nonlinear intensity of the drive system is inversely proportional to the number of meshing movable teeth. It was also noted that the rotor is most affected by the nonlinear phenomenon. These results can be utilized both to optimize the dimensions of the piezoelectric precision drive system and to reduce the intensity of vibrations during operation.