  Under suitable conditions a flow on a torus $C^{(p)}$--close, with $p$ large
enough, to a quasi periodic diophantine rotation is shown to be conjugated to
the quasi periodic rotation by a map that is analytic in the perturbation size.
This result is parallel to Moser's theorem stating conjugability in class
$C^{(p')}$ for some $p'<p$. The extra conditions restrict the class of
perturbations that are allowed.
