  Let $F$ be a function field of characteristic $p>0$, $\F/F$ a Galois
extension with $Gal(\F/F)\simeq \Z_l^d$ (for some prime $l\neq p$) and $E/F$ a
non-isotrivial elliptic curve. We study the behaviour of Selmer groups
$Sel_E(L)_r$ ($r$ any prime) as $L$ varies through the subextensions of $\F$
via appropriate versions of Mazur's Control Theorem. As a consequence we prove
that $Sel_E(\F)_r$ is a cofinitely generated (in some cases cotorsion)
$\Z_r[[Gal(\F/F)]]$-module.
