Two-stage stochastic programs with random right-hand side are considered. O
ptimal values and solution sets are regarded as mappings of the expected re
course functions and their perturbations, respectively. Conditions are iden
tified implying that these mappings are directionally differentiable and se
midifferentiable on appropriate functional spaces. Explicit formulas for th
e derivatives are derived. Special attention is paid to the role of a Lipsc
hitz condition for solution sets as well as of a quadratic growth condition
of the objective function.