The capture, the structuring and the exploitation of competences of an "object" (like a business partner, an employee, a software component, a Web service, etc.) are crucial problems in various applications, like cooperative and distributed applications or e\_business applications. The work we describe here concerns competence advertising, organization, discovery and composition. Indeed, one of the originality of the proposal is in the nature of the answers the intended system can return when seeking for individuals fitted with given competences: answers may be composite ones in that sense that when no single object meets the search criteria, we attempt to find out what a set of objects, when pooled together, do satisfy the whole search criteria. Conceptual Graphs (CGs) are used as a knowledge representation formalism and operations on graphs are used as a search mechanism. A client/server prototype, viewed as a federation of mediators, has been developed as a proof of concept.