  Axial oscillations relevant to the r-mode instability are studied with slow
rotation formalism in general relativity. The approximate equation governing
the oscillations is derived with second-order rotational corrections. The
equation contains an effective 'viscosity-like' term, which originates from
coupling to the polar g-mode displacements. The term plays a crucial role on
the resonance point, where the disturbance on the rotating stars satisfies a
certain condition at the lowest order equation. The effect is significant for
newly born hot neutron stars, which are expected to be subject to the
gravitational radiation driven instability of the r-mode.
