  In this work we present results for pairing gaps in $\beta$--stable neutron
star matter with electrons and muons using a relativistic
Dirac--Brueckner--Hartree--Fock approach, starting with modern meson--exchange
models for the nucleon--nucleon interaction. Results are given for
superconducting $^1S_0$ protons and $^3P_2$ and $^1D_2$ neutron superfluids. A
comparison is made with recent non--relativistic calculations and the
implications for neutron star cooling are discussed.
