Abstract. Data exchanges between Web services engaged in a composition raise several heterogeneities. In this paper, we address the problem of data cardinality heterogeneity in a composition. Firstly, we build a theoretical framework to describe different aspects of Web services that relate to data cardinality, and secondly, we solve this problem by developing a solution for cardinality mediation based on constraint logic programming. Keywords. Web services, Composition, Mediation, Cardinality.