  We compute the Z-rank of the subgroup of elements of the multiplicative group
of a number field K that are norms from every finite level of the cyclotomic
Z{\ell}-extension of K. Thus we compare its {\ell}-adification with the group
of logarithmic units of K. By the way we point out an easy proof of the
Gross-Kuz'min conjecture for {\ell}-undecomposed extensions of abelian fields.
