  Using time evolutions of the relevant linearised equations we study
non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars.
We consider perturbations of Newtonian axisymmetric background configurations
and account for the presence of superfluid components via the standard
two-fluid model. Within the Cowling approximation, we are able to carry out
evolutions for uniformly rotating stars up to the mass-shedding limit. This
leads to the first detailed analysis of superfluid neutron star oscillations in
the fast rotation regime, where the star is significantly deformed by the
centrifugal force. For simplicity, we focus on background models where the two
fluids (superfluid neutrons and protons) co-rotate, are in beta-equilibrium and
coexist throughout the volume of the star. We construct sequences of rotating
stars for two analytical model equations of state. These models represent
relatively simple generalisations of single fluid, polytropic stars. We study
the effects of entrainment, rotation and symmetry energy on non-radial
oscillations of these models. Our results show that entrainment and symmetry
energy can have a significant effect on the rotational splitting of
non-axisymmetric modes. In particular, the symmetry energy modifies the
inertial mode frequencies considerably in the regime of fast rotation.
