Conformally Covariant Bi-Differential Operators on a Simple Real Jordan Algebra

For a simple real Jordan algebra $V,$ a family of bi-differential operators from ${\mathcal{C}}^{\mathrm{\infty }}(V\times V)$ to ${\mathcal{C}}^{\mathrm{\infty }}(V)$ is constructed. These operators are covariant under the rational action of the conformal group of $V\mathrm{.}$ They generalize the classical {\em Rankin-Cohen} brackets (case $V=\mathbb{R}$).