  Let $X$ be the wonderful compactification of a complex symmetric space $G/H$
of minimal rank. For a point $x\,\in\, G$, denote by $Z$ be the closure of
$BxH/H$ in $X$, where $B$ is a Borel subgroup of $G$. The universal cover of
$G$ is denoted by $\widetilde{G}$. Given a $\widetilde{G}$ equivariant vector
bundle $E$ on $X,$ we prove that $E$ is nef (respectively, ample) if and only
if its restriction to $Z$ is nef (respectively, ample). Similarly, $E$ is
trivial if and only if its restriction to $Z$ is so.
