  An affine variety $X$ of dimension $\ge 2$ is called {\em flexible} if its
special automorphism group SAut$(X)$ acts transitively on the smooth locus
$X_{reg}$ \cite{AKZ}. Recall that the special automorphism group SAut$(X)$ is
the subgroup of the automorphism group Aut$(X)$ generated by all one-parameter
unipotent subgroups \cite{AKZ}. Given a normal, flexible, affine variety $X$
and a closed subvariety $Y$ in $X$ of codimension at least 2, we show that the
pointwise stabilizer subgroup of $Y$ in the group SAut$(X)$ acts infinitely
transitively on the complement $X\backslash Y$, that is, $m$-transitively for
any $m\ge 1$. More generally we show such a result for any quasi-affine variety
$X$ and codimension $\ge 2$ subset $Y$ of $X$. In the particular case of
$X=\AA^n$, $n\ge 2$, this yields a Theorem of Gromov and Winkelmann \cite{Gr1},
\cite{Wi}.
