  We develop a Lagrangian perturbation framework for rotating non-relativistic
superfluid neutron stars. This leads to the first generalization of classic
work on the stability properties of rotating stars to models which account for
the presence of potentially weakly coupled superfluid components. Our analysis
is based on the standard two-fluid model expected to be relevant for the
conditions that prevail in the outer core of mature neutron stars. We discuss
the implications of our results for dynamical and secular instabilities of a
simple neutron star model in which the two fluids are allowed to assume
different (uniform) rotation rates.
