Uncertainty is very important in risk analysis. A natural way to describe this uncertainty is to describe a set of possible values of each unknown quantity (this set is usually an interval), plus any additional information that we may have about the probability of different values within this set. Traditional statistical techniques deal with the situations in which we have a complete information about the probabilities; in real life, however, we often have only partial information about them. We therefore need to describe methods of handling such partial information in risk analysis. Several such techniques have been presented, often on a heuristic basis. The main goal of this paper is to provide a justification for a general second-order formalism for handling different types of uncertainty.