  Following the works of Y. Benoist, P. Foulon and F. Labourie \cite{BFL}, and
having in mind the standing conjecture about the algebricity of Anosov actions
of $\mathbb{R}^k$, we propose some geometrical conditions which generalize the
notion of contact structures and prove that Anosov actions associated with such
structures are conjugated to an Affine action. We also construct two families
of examples, the first one is algebraic in nature, and the second one imposes
some dynamical conditions instead of geometrical ones.
