of the tensor virial method is based on Ref. [@SW2000].

This review is organized as follows. In the remainder of the Introduction we motivate the averaged superfluid hydrodynamics and identify the relevant scales in the problem. In Sect. 2 we give a tutorial introduction to the Newtonian superfluid hydrodynamics, which is mainly built on the work of Bekarevich and Khalatnikov [@BK]. Sect. 3 introduces the tensor virial method and illustrates its applications to the superfluid ellipsoidal figures by computing the perturbations of the new terms in virial equations due to their two-fluid nature. We discuss in Sect. 4 the oscillations of superfluid Maclaurin spheroids including the effects of mutual friction and viscosity of the normal fluid. Sect. 5 is a brief summary. We refer the reader to the accompanying article by B. Carter for a review of relativistic models and an overview of the state of the art of the theory of superfluidity in neutron stars.

Characteristic length scales
----------------------------

The physics of neutron star superfluidity unfolds on a hierarchy of three distinct length-scales. The separation of these scales is useful, as often the physics of a neighboring scale enters a theory at a given scale in the form of 