This paper aims at explaining the semantic behaviour of French modal verbs devoir (‘must’) and pouvoir (‘can’, ‘may’) with the hypothesis that they are conceptual, not procedural, and semantically under-determined. We suggest that these verbs are not polysemous if considering polysemy in the technical sense implying a conventionalization of several meanings in the lexicon. We try to show that the various meanings of these verbs are not all reducible to one of the canonical cases usually considered in the literature. We suggest that all meanings of these verbs emerge as pragmatic enrichments on the basis of an underspecified notion of possibility or necessity.