Abstract <p> Two approaches to the problem of triaxial stabilization of a rigid body with the aid ofdelayed feedback law are considered. The first approach is based on choosing control as a sum ofdissipative and restoring torques with a constant delay in the restoring torque. In this case, aspecial construction of Lyapunov–Krasovskii functional is used to derive exponential stabilityconditions of the programed regime. In the second approach, the control is constructed withoutusing a dissipative torque. The stabilization is ensured via artificially introducing a delay in therestoring torque, and the proof of the exponential stability is based on the application of theRazumikhin method.</p>