We consider the experimental design problem of selecting values of design variables x for observation of a response y that depends on x and on model parameters $ heta$. The form of the dependence may be quite general, including all linear and nonlinear modeling situations. The goal of the design selection is to efficiently estimate functions of $ heta$. Three new criteria for selecting design points x are presented. The criteria generalized the usual Bayesian optimal design criteria to situations n which the prior distribution for $ heta$ amy be uncertain. We assume that there are several possible prior distributions,. The new criteria are applied to the nonlinear problem of designing to estimate the turning point of a quadratic equation. We give both analytic and computational results illustrating the robustness of the optimal designs based on the new criteria.