abstract: Lp-cohomology is a potentially interesting quasi-isometric invariant. For rank-one simple Lie groups, it has been studied in detail by Pansu. In higher rank, its study is less developed. Motivated by some questions by Gromov, we show that for p large enough, the Lp-cohomology is null in degree larger than the rank and non-null in degree equal to the rank. These results extend also to certain Lie groups of type AN. (Joint work with Bertrand Rémy).