In this paper we study differential inclusions with boundary conditions in which the vector field F(t,x,y) is a multifunction with Caratheodory type conditions. We consider, first, the case which F has values in and we establish the existence of extremal solutions in the order interval determined by the lower and the upper solution. Then we prove the existence of solutions for a Dirichlet problem in the case in which F takes their values in a Hilbert space.