An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory to characterize uncertainty neutrality and different degrees of uncertainty aversion. Coauthors are Hans Jorgen Jacobsen, Birgitte Sloth, and Torben Tranaes. Copyright 1994 by Kluwer Academic Publishers