The averaging analysis was carried out to study the motion of a quasi-axisymmetrical gyrostat under a small-magnitude self-excited control torque. The common approach to investigating the problem of rigid body rotation under the action of a small torqueknown in the body frame was described. Using this approach, the problem (Grammels problem for the case of small torque) that ismaintaining the angular velocity of a quasi-axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.