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Let $F$ be a function field of characteristic $p\>0$, $ℱ/F$ a ${\mathbb{Z}}_l^d$-extension (for some prime $l\ne p$) and $E/F$ a non-isotrivial elliptic curve. We study the behaviour of the $r$-parts of the Selmer groups ($r$ any prime) in the subextensions of $ℱ$ via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of $ℱ/F$.