The inertial continuously variable transmissions are transmissions of mechanical type. They have a number of advantages in comparison with other types of transmissions. For example, they have a big value of the coefficient of efficiency, since the principle of their action does not imply the need to convert energy from one type to another one. These transmissions have a compact design, a wide range of torque transformation. They can operate in direct mode, smoothing the torsional vibrations in the system. At the moment when the output shaft is stopped, the input transmission shaft continues to rotate, that prevents the engine from overloading. There are other advantages. But despite these advantages, the inertial transmissions are not widely used in the automotive industry. The main reason for this is the inadequate durability of the freewheel mechanisms involved in the designs of the inertial transmissions. The paper considers some ways to improve the efficiency and durability of the inertial transmissions. Dynamics of the inertial transmissions is considered. For this purpose, physical and mathematical models of the inertial transmissions have been developed. The transmissions have a variable structure, nevertheless, new mathematical methods have been developed in the paper, which made it possible to describe the dynamics of the transmissions in the form of only one system of differential equations. On the basis of the developed mathematical model, periodic solutions of the system are constructed, and the external characteristic of the inertial transmissions is obtained. It is shown that the obtained external characteristic is close to ideal one. To increase the reliability and durability of the inertial transmissions, a new design of the overrunning clutches is proposed, which is distinguished by increased capacity of operating. The proposed design has a new principle of activity. It is shown that the load on the details of the developed overrunning clutches can be reduced in several times in comparison with the existing designs of overrunning clutches. A mathematical model of the proposed design of the overrunning clutches is investigated in this paper. Periodic solutions of the systems of differential equations that describe the dynamics of the overrunning clutches with the new principle of action are constructed. It is shown that the application of the proposed design allows increasing significantly the durability of the inertial transmissions. In this paper computer simulation was carried out, which confirmed the correctness of the results of the theoretical studies.