Multilingual natural language processing (NLP), whether it concerns analysis or generation of sentences, requires a sound language-independent representation for grasping the deep meaning of narratives. The formalism of conceptual graphs (CGs), especially designed to cope with natural language semantics, constitutes a good repository for dealing with the compositionality and intricacies of medical language. This paper describes our experiment, as part of the European GALEN project, for exploiting a conceptual graph representation of medical language, upon which multilingual medical language processing is performed.