This paper proposes a model for Information Retrieval (IR) based on possibilistic directed networks. Relations documents-terms and query-terms are modeled through possibility and necessity measures rather than a probability measure. The relevance value for the document given the query is measured by two degrees: the necessity and the possibility. More precisely, the user’s query triggers a propagation process to retrieve necessarily or at least possibly relevant documents. The possibility degree is convenient to filter documents out from the response (retrieved documents) and the necessity degree is useful for document relevance confirmation. Separating these notions may account for the imprecision pervading the retrieval process. Moreover, an improved weighting of terms in a query not present in the document is introduced. Experiments carried out on a sub-collection of CLEF, namely LeMonde 1994, a French newspapers collection, showed the effectiveness of the model.