  We develop a general formalism to treat, in general relativity, the nonradial
oscillations of a superfluid neutron star about static (non-rotating)
configurations. The matter content of these stars can, as a first
approximation, be described by a two-fluid model: one fluid is the neutron
superfluid, which is believed to exist in the core and inner crust of mature
neutron stars; the other fluid is a conglomerate of all charged constituents.
We use a system of equations that governs the perturbations both of the metric
and of the matter variables, whatever the equation of state for the two fluids.
The entrainment effect is explicitly included. We also allow for an outer
envelope composed of ordinary fluid. We derive and implement the junction
conditions for the metric and matter variables at the core/envelope interface.
We investigate how the quasinormal modes of a superfluid star are affected by
changes in the entrainment parameter, and unveil a series of avoided crossings
between the various modes. We provide a proof that all modes of a two-fluid
star must radiate gravitationally. We also discuss the future detectability of
pulsations in a superfluid star and argue that it may be possible to use
gravitational-wave data to constrain the parameters of superfluid neutron
stars.
