  A real algebraic plane curve $A$ is said to be dividing if its real part
$\mathbb{R}A$ disconnects its complex part $\mathbb{C}A$. A pencil of curves is
totally real with respect to $A$ if it has only real intersections with
$\mathbb{C}A$. If there exists such a pencil, then $A$ is dividing, this is the
case for the $M$-curves. Can conversely any dividing curve be endowed with a
totally real pencil? We study here the case of $M-2$-sextics having 2 or 6
empty exterior ovals. Such sextics are always dividing. We prove that they may
actually be endowed with a totally real pencil of cubics.
