Let f1, f2 be holomorphic endomorphisms of P k, of degrees d1 ≥ 2, d2 ≥ 2. Assume that f1◦f2 = f2◦f1 and that d1 1 6= d2 2 for all integers n1, n2. We then show that fj are critically finite. Moreover there is an orbifold (Pk, n) such that f1, f2 are coverings of (P k, n). In the P2 case we give the list of commuting pairs satisfying the above conditions.