The new Expected Uncertain Utility (EUU) theory is introduced and analyzed. According to this theory each decision maker has a prior \(\mu\) on a \(\sigma\)-algebra \(\mathcal{E}\) and an interval utility \(u=u(x,y)\). Each act \(f\) can be ideal or non-ideal. Ideal act is \(\mathcal{E}\)-measurable. The utility of an ideal act \(f\) is \[ W(f)=\int u(f,f)\,\text{d}\mu. \] For a non-ideal act \(f\) the agent forms an ideal lower bound \([f]_1\) and an ideal upper bound \([f]_2\). The utility of such act \(f\) is \[ W(f)=\int u([f]_1,[f]_2)\,\text{d}\mu. \] The decision maker transforms each uncertain prospect into an interval-valued prospect that assigns an interval of prizes to each state. Then the decision maker classifies all prospects in accordance with their expected interval utilities. The model of EUU theory is presented with all required axioms. The representation theorem is provided. Comparative measures of uncertainty aversion and uncertainty of events are defined. The relation of these measures with model parameters are derived. The related works are discussed extensively. All assertions of the main text are presented together with their proofs in appendices. Despite its closeness to subjective expected utility theory, EUU theory is flexible enough to accommodate Ellsberg-style and Allais-style evidence.