  We present solutions of the coupled, non-relativistic $^3S_1$-$^3D_1$ gap
equations for neutron-proton pairing in symmetric nuclear matter, and estimate
relativistic effects by solving the same gap equations modified according to
minimal relativity and using single-particle energies from a
Dirac-Brueckner-Hartree-Fock calculation. As a main result we find that
relativistic effects decrease the value of the gap at the saturation density
$k_F=1.36 fm^{-1}$ considerably, in conformity with the lack of evidence for
strong neutron-proton pairing in finite nuclei.
