Generalized Ornstein-Uhlenbeck semi-groups on stratified groups Let G = exp G be a stratified group with dilation δ. Let (Xi) n i=1 be a basis of the first layer of G, ∇f = (Xif) n i=1, let L = − Pn i=1 X2 i be the subLaplacian and let p be the (heat) kernel of e −L. We consider the semi-groups defined on L q (pdg) by e −t∇∗∇ and e −tN f(γ) = Z G f(δe−tγδ√ 1−e−2t g)p(g)dg.