Let M be the multilinear maximal function and →b =(b1,· · ·,bm)be a collection of locally integrable functions.Denote by M→b and [→b,M] the maximal commutator and the commutator of M with →b.In this paper,the multiple weighted strong and weak-type estimates for operators M→b and [→b,M] are studied.Some characterizations of the class of functions bj are given,for which these operators satisfy some strong or weak type estimates.