The capture, the structuring of the expertise or competences of an " object " (like a business partner , an employee, a software component, a Web service, etc.) are crucial problems in many domains , like cooperative and distributed applications or e business applications. The work we describe in this paper concerns the advertising and the discovery of competences. We found our proposals on Conceptual Graphs (for representing the com-petences) and their related operations for the competence discovery and composition processes.