A magnetic nucleus located on an internal rotor can interact with magnetic fields arising from end-over-end molecular rotation as well as internal rotation. In this paper the expressions for spin-rotational relaxation times, $T_{1.SR};and;T_{2.SR}$, are derived for such nucleus with the anisotropy of molecular rotation explicitly taken into consideration. The derived expressions are shown to be composed of two parts, the contribution from spin-overall-rotation coupling and that from spin-internal-rotation coupling. Some remarks on the use of derived expressions are also provided.