  We demonstrate a possibility of existence of a peculiar temperature-dependent
composition $g$-modes in superfluid neutron stars. We calculate the
Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ frequency for these modes,
as well as their eigenfrequencies. The latter turn out to be rather large, up
to $\sim 500$ Hz for a chosen model of a neutron star. This result indicates,
in particular, that use of the barotropic equation of state may be not a good
approximation for calculation of inertial modes even in most rapidly rotating
superfluid neutron stars.
