The problem of triaxial orientation of a rigid body under the action of restoring and dissipative torques is considered. It is assumed that the dissipative torque evolves with time, and the evolution results in unbounded increasing of the torque. Both the cases of linear dissipative torque and nonlinear homo-geneous one are considered. Conditions are determined under which one can guarantee asymptotic stability of a programmed motion of the body despite the evolution of the dissipative torque. The effectiveness of the proposed results is illustrated using simulation examples.