Abstract. The paper deals with the minimization of an integral functional over an L^p space subject to various types of constraints. For such optimization problems new necessary optimality conditions are derived, based on several concepts of nonsmooth analysis. In particular, we employ the generalized differential calculus of Mordukhovich and the fuzzy calculus of proximal subgradients. The results are specialized to nonsmooth two-stage and multistage stochastic programs.