of gravitational wave radiation, which are expected to be detectable by future laser interferometer detectors. It is hoped that one can probe neutron star interiors and their superfluidity using gravity waves, as their eigen-frequencies and damping may depend on the dissipation in the superfluid, at temperatures below the superfluid phase transition.

This review concentrates on the oscillations of superfluid self-gravitating ellipsoids within the tensor virial method. The method was originally introduced by Chandrasekhar and Fermi in the context of magneto-hydrodynamics [@CHANDRA_FERMI]. It was extensively developed in the 1960s by Chandrasekhar for the study of the ellipsoidal figures of equilibrium and their oscillations. A comprehensive account of this work is contained in Chandrasekhar’s monograph [*Ellipsoidal Figures of Equilibrium*]{} (hereafter EFE)[@CHANDRA].

The ellipsoidal approximation provides an idealized picture of oscillations of neutron stars. One can think of several arguments in favor of adopting such an approach: first, the combination of the Newtonian gravity and two-fluid hydrodynamics of superfluid defines an exactly solvable model if we assume that the fluids are incompressible and inviscid; second, past experience with single-fluid self-gravitating ellipsoids shows that most of the qualitative features found for these ellipsoids have their analogs in more “realistic” systems; third, the method is 