Abstract. In this paper we study the effective behavior of composites with a nonlinear material behavior and a special type of microstructure. The microstructure we study is obtained by reiteration, i.e., introducing several local scales. We derive bounds on the effective shear properties and prove that the bounds are sharp when the number of scales tends to infinity.

AMS Subject Classification (1991): 35B27, 73B27

Received November 17, 1998, and in revised form April 12, 1999. (Registered under 2702/2009.)