This paper deals with preference representation and elicitation in the context of multiattribute utility theory under risk. Assuming the decision maker behaves according to the EU model, we investigate the elicitation of generalized additively decomposable utility functions on a product set (GAI-decomposable utilities). We propose a general elicitation procedure based on a new graphical model called a GAI-network. The latter is used to represent and manage independences between attributes, as junction graphs model independences between random variables in Bayesian networks. It is used to design an elicitation questionnaire based on simple lotteries involving completely specified outcomes. Our elicitation procedure is convenient for any GAI-decomposable utility function, thus enhancing the possibilities offered by UCP-networks.