The gyroscopic devices are primary arrangements for navigation and control systems that the contemporary aerospace, ships and other industries have been widely adopted. The main remarkable property of the gyroscope is represented in permanent maintaining the axis of a spinning rotor in a space. This gyroscope property is the result of action of the several internal inertial torques produced by the external load torque. Internal inertial torques of the gyroscope are generated by action of the components of centrifugal, common inertial and Coriolis forces as well as the change in the angular momentum. These inertial forces are produced by rotating mass elements and the center mass of the spinning rotor. The action of all gyroscope's internal torques are interrelated simultaneously around gyroscope axes, and are manifested the resistance and precession torques. The designers of gyroscopic devices can compute their acting forces and motions based on equations of the internal torques. However, gyroscope's inertial torques possess several properties, which correct usage enables getting correct results in computing of gyroscope parameters. This manuscript describes the properties of the inertial torques acting on a gyroscope that should be used for mathematical models of the gyroscope motions.