We study decision problems in which consequences of the various alternative actions depend on states determined by a generative mechanism representing some natural or social phenomenon. Model uncertainty arises because decision makers may not know this mechanism. Two types of uncertainty result, a state uncertainty within models and a model uncertainty across them. We discuss some two-stage static decision criteria proposed in the literature that address state uncertainty in the first stage and model uncertainty in the second (by considering subjective probabilities over models). We consider two approaches to the Ellsberg-type phenomena characteristic of such decision problems: a Bayesian approach based on the distinction between subjective attitudes toward the two kinds of uncertainty; and a non-Bayesian approach that permits multiple subjective probabilities. Several applications are used to illustrate concepts as they are introduced.