  The thermal evolution of Neutron Stars is affected by the elementary
excitations that characterize the stellar matter. In particular, the low-energy
excitations, with a spectrum linear in momentum, can play a major role in the
emission and propagation of neutrinos. In this paper, we focus on the
elementary modes in the region of proton superfluidity, where the neutron
component is expected to have a very small or zero pairing gap.
  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 in order to
describe the response of a superfluid system. The formalism we use ensures that
the Generalized Ward's Identities are satisfied. Despite their relative small
fraction, the protons turn out to modify the neutron spectral function as a
consequence of the nuclear neutron-proton interaction. This effect is
particularly evident at the lower density, just below the crust for a density
close to the saturation value, while at increasing density the neutrons and the
protons are mainly decoupled. The proton spectral function is characterized by
a pseudo-Goldstone mode below $ 2\Delta $, twice the pairing gap, and a
pair-breaking mode above $ 2\Delta $. The latter merges in the sound mode of
the normal phase at higher momenta. The neutron spectral function develops a
collective sound mode only at the higher density. The electrons have a strong
screening effect on the proton-proton interaction at the lower momenta, and
decouple from the protons at higher momenta.
