  Iwasawa's classical asymptotical formula relates the orders of the $p$-parts
$X_n$ of the ideal class groups along a $\ZM_p$-extension $F_\infty/F$ of a
number field $F$, to Iwasawa structural invariants $\la$ and $\mu$ attached to
the inverse limit $X_\infty=\limpro X_n$. It relies on "good" descent
properties satisfied by $X_n$. If $F$ is abelian and $F_\infty$ is cyclotomic
it is known that the $p$-parts of the orders of the global units modulo
circular units $U_n/C_n$ are asymptotically equivalent to the $p$-parts of the
ideal class numbers. This suggests that these quotients $U_n/C_n$, so to speak
unit class groups, satisfy also good descent properties. We show this directly,
i.e. without using Iwasawa's Main Conjecture.
