  The longitudinal and transverse nuclear magnetic relaxation rates $1/T_1(T)$
and $1/T_2(T)$ are calculated for three- and two-dimensional (3D and 2D)
metallic ferro- and antiferromagnets (FM and AFM) with localized magnetic
moments in the spin-wave temperature region. The contribution of the one-magnon
decay processes is strongly enhanced in comparison with the standard $T$-linear
Korringa term, especially for the FM case. For the 3D AFM case this
contribution diverges logarithmically, the divergence being cut at the magnon
gap $\omega_0$ due to magnetic anisotropy, and for the 2D AFM case as
$\omega_0^{-1}$. The electron-magnon scattering processes yield $T^2\ln
(T/\omega_0)$ and $T^2/\omega_0^{1/2}$-terms in $1/T_1$ for the 3D AFM and 2D
FM cases, respectively. The two-magnon (``Raman'') contributions are
investigated and demonstrated to be large in the 2D FM case. Peculiarities of
the isotropic 2D limit (where the correlation length is very large) are
analyzed.
