  Let f_1, f_2 be holomorphic endomorphisms of P^k, of degrees d_1\geq 2,
d_2\geq 2. Assume that f_1\circ f_2=f_2\circ f_1 and that d_1^{n_1}\not
=d_2^{n_2} for all integers n_1, n_2. We then show that f_j are critically
finite. Moreover there is an orbifold (P^k,n) such that f_1, f_2 are coverings
of (P^k,n). In the P^2 case we give the list of commuting pairs satisfying the
above conditions.
