  We present results concerning adiabatic inertial-mode oscillations of
non-stratified superfluid neutron stars in Newtonian gravity, using the
anelastic and slow-rotation approximations. We consider a simple two-fluid
model of a superfluid neutron star, where one fluid consists of the superfluid
neutrons and the second fluid contains all the comoving constituents (protons,
electrons). The two fluids are assumed to be ``free'' in the sense that
vortex-mediated forces like mutual friction or pinning are absent, but they can
be coupled by the equation of state, in particular by entrainment. The
stationary background consists of the two fluids rotating uniformly around the
same axis with potentially different rotation rates. We study the special cases
of co-rotating backgrounds, vanishing entrainment, and the purely toroidal
r-modes, analytically. We calculate numerically the eigenfunctions and
frequencies of inertial modes in the general case of non co-rotating
backgrounds, and study their dependence on the relative rotation rate and
entrainment. In these non-stratified models we find avoided crossings only
between associated mode-pairs, eg. an ``ordinary'' mode and its ``superfluid''
counterpart, while other mode-frequencies generally cross as the background
parameters are varied. We confirm (for the first time in a mode calculation)
the onset of a ``two-stream instability'' at a critical relative background
rotation rate, and study some of the properties of this instability for the
inertial modes.
