N)N, L2div(R

Abstract. Nguetseng's notion of two-scale convergence and some of its main proper-ties are rst shortly reviewed. The (weak) two-scale limit of the gradient of bounded sequences of W 1;p(RN) is then studied: if u " ! u weakly in W 1;p(RN), a sequence fu1"g is constructed such that u1"(x) ! u1(x; y) and ru"(x) ! ru(x) +ryu1(x; y) weakly two-scale. Analogous constructions are introduced for the weak two-scale limit of derivatives in the spaces W 1;p(RN)N, L2rot(