The inertial continuously variable transmissions are mechanical transmissions that are based on the principle of inertia. These transmissions have a lot of advantages. Usually, the design of the inertial continuously variable transmissions consists of inertia pulsed mechanism with unbalanced inertial elements and two overrunning clutches. Dynamics of the transmissions is described by systems of substantial nonlinear differential equations. In general, precise methods of solution for such equations do not exist. Therefore, in practice, approximate analytical and numerical methods must be employed. The main analytical methods employ successive approximation, a small parameter, or power series expansion. Each approach has its advantages and disadvantages. Therefore, we need to compare them in order to select the best method for dynamic study of such kind of transmissions. In this paper a comparative analysis of approximate methods of solving of differential equations for the inertial continuously variable transmissions is done. The object of the investigation is structural dynamics of the continuously variable automatic inertial mechanical transmissions. Approximate methods of solving the nonlinear differential equations of motion of inertial transmissions based on a pulsed mechanism are compared. These methods take account of the nonuniform driveshaft rotation and the dynamic characteristics of the motor. Analysis of the solutions reveals the best method for dynamic study of the given transmissions. The comparative analysis showed that the best method of approximate solution is the method of a small parameter.