  Let $C$ be a smooth curve of genus $g \geq 2$ on $\C$. Let $L$ be a line
bundle on $C$ generated by its global sections and let $E_{L}$ be the dual of
the kernel of the evaluation map $e_{L}$. We are studying here the relation
between the stability the fact that the bundle is verifying a condition $(R)$
introduced by Raynaud : we prove that $E_{L}$ is semi stable when $C$ is
general. We also prove that $E_{L}$ is verifying $(R)$ when $\deg(L) \geq 2g$
or when $L$ is generic. Finally we prove that for each $p$ in $\{2,...,
\mathrm{rg}(E_{L})-2\}$, if $\deg(L) \geq 2g+2$ then $\Lambda^{p}E_{L}$ is not
verifying $(R)$.
