  The coexistence of ferromagnetism and superconductivity in
RuSr$_2$GdCu$_2$O$_8$ was reported both from experiments (by Tallon et. al.)
and first-principles calculations (by Pickett et. al.). Here we report that our
first-principles full-potential linearized augmented plane wave (FLAPW)
calculations, employing the precise crystal structure with structural
distortions (i.e., RuO$_6$ rotations) determined by neutron diffraction,
demonstrate that antiferromagnetic ordering of the Ru moments is energetically
favored over the previously proposed ferromagnetic ordering. Our results are
consistent with recently performed magnetic neutron diffraction experiments
(Lynn et. al). Ru $t_{2g}$ states, which are responsible for the magnetism,
have only a very small interaction with Cu $e_g$ states, which results in a
small exchange splitting of these states. The Fermi surface, characterized by
strongly hybridized $dp\sigma$ orbitals, has nesting features similar to those
in the two-dimensional high $T_c$ cuprate superconductors.
