The paper deals with the problem of monoaxial attitude stabilization of a rigid body. The possibility of implementing such a control system in which the restoring torque tends to zero as time increases is studied. With the aid of the Lyapunov direct method and the differential inequalities theory, conditions under which an equilibrium position of the body is stable with respect to all variables as well as with respect to a part of variables are derived. The results of a numerical modeling are presented to demonstrate the effectiveness of the proposed approaches.