We present in this report some results about the convergence of the multi-linear homogeneous sums of random variables (also called Chaotic Polynomial), following the invariance principle recently established by Mosset, O'Donnel and Oleszkiewicz [2], the universality principle developed by Nourdin, Pecatti and Reinert in [3] , and the results developed by Déya and Nourdin in the free probability framework [1]. Moreover, we provide au extension of these results by defining an interesting family of these Chaotic Polynomials which have the same but no gaussian or semicircular asymptotically distribution.