Parameter sensitivity analysis of a two-level design optimization problem can be decomposed into two levels. In the first-level, the sensitivities of the subproblems are calculated separately. In the second-level, the sensitivities obtained for the first-level subproblems are co-ordinated to obtain the overall sensitivity information. Using this approach, we can not only obtain the overall effect that a small change in a parameter has on the optimum solution of a problem (or system) but also its local effects on the subproblems (or subsystems). A simple two-bar truss example demonstrates the approach.