The article proposes a classification of the different uses of the French modal verbs pouvoir and devoir. The author starts from the hypothesis that these verbs have an underdetermined signification which permits them to have many different uses through their interaction with the co(n)text. The paper distinguishes three levels of analysis: agentive modality of doing, non-agentive modality of being and a postmodal level. At each level, the relation between modality and evidentiality is discussed. At the modality of doing level, pouvoir and devoir, cannot be evidential operators because of their scope, while at the modality of being level, inferential evidentiality and epistemic modality are intrinsically related. Concerning the postmodal uses, the paper observes the absence of an evidential use of reported information for devoir and suggests that pouvoir has an (ad)mirative use.