  We discuss spin and pseudo-spin symmetry in the spectrum of single nucleons
and single anti-nucleons in a nucleus. As an example we use relativistic mean
field theory to investigate single anti-nucleon spectra. We find a very well
developed spin symmetry in single anti-neutron and single anti-proton spectra.
The dominant components of the wave functions of the spin doublet are almost
identical. This spin symmetry in anti-particle spectra and the pseudo-spin
symmetry in particle spectra have the same origin. However it turns out that
the spin symmetry in anti-nucleon spectra is much better developed than the
pseudo-spin symmetry in normal nuclear single particle spectra.
