A rigid body forced by a nonstationary perturbing torque with zero mean value is under consideration. The control strategy for attitude stabilization of the rigid body is based on the usage of dissipative and restoring torques. It is assumed that the dissipative torque is linear, while restoring and perturbing torques are purely nonlinear. A theorem on sufficient conditions for asymptotic stability of the body angular position is proved on the basis of the decomposition method, the Lyapunov direct method and the averaging technique. Computer simulation results illustrating the theorem are presented.