Abstract: Managing multiple ontologies is now a core question in most of the applications that require semantic interoperability. The semantic web is surely the most significant application of this report: the current challenge is not to design, develop and deploy domain ontologies but to define semantic correspondences among multiple ontologies covering overlapping domains. In this paper, we introduce a new approach of ontology matching named axiom-based ontology matching. As this approach is founded on the use of axioms, it is mainly dedicated to heavyweight ontologies, but it can also be applied to lightweight ontologies as a complementary approach to the current techniques based on the analysis of natural language expressions, instances and/or taxonomical structures of ontologies. This new matching paradigm is defined in the context of the conceptual graphs model, where the projection (i.e. the main operator for reasoning with conceptual graphs which corresponds to homomorphism of graphs) is used as a means to semantically match the concepts and the relations of two ontologies through the explicit representation of the axioms in terms of conceptual graphs. We also introduce an ontology of representation, called MetaOCGL, dedicated to the reasoning of heavyweight ontologies at the meta-level.