  Several phenomena occurring in neutron stars are affected by the elementary
excitations that characterize the stellar matter. In particular, low-energy
excitations can play a major role in the emission and propagation of neutrinos,
neutron star cooling and transport processes. In this paper, we consider the
elementary modes in the star region where both proton and neutron components
are superfluid.
  We study the overall spectral functions of protons, neutrons and electrons on
the basis of the Coulomb and nuclear interactions.
  This study is performed in the framework of the Random Phase Approximation,
generalized to superfluid systems. The formalism we use ensures that the
Generalized Ward's Identities are satisfied. We focus on the coupling between
neutrons and protons. On one hand this coupling results in collective modes
that involve simultaneously neutrons and protons, on the other hand it produces
a damping of the excitations. Both effects are especially visible in the
spectral functions of the different components of the matter. At high density
while the neutrons and protons tend to develop independent excitations, as
indicated by the spectral functions, the neutron-proton coupling still produces
a strong damping of the modes.
