  This review starts with a discussion of the hierarchy of scales, relevant to
the description of superfluids in neutron stars, which motivates a subsequent
elementary exposition of the Newtonian superfluid hydrodynamics. Starting from
the Euler equations for a superfluid and a normal fluid we apply the tensor
virial method to obtain the virial equations of the first, second, and third
order and to compute their Eulerian perturbations. Special emphasis is put on
the computation of perturbations of the new terms due to mutual gravitational
attraction and mutual friction between the two fluids. The oscillation modes of
superfluid Maclaurin spheroids are derived from the first and second order
perturbed virial equations. We discuss two generic classes of oscillation modes
which correspond to the co-moving and relative oscillations of two fluids.
These modes decouple if the normal fluid is inviscid. We also discuss the
mixing of these modes (when the normal fluid is viscous) and its effect on the
dynamical and secular instabilities of the co-moving modes and their damping.
