This paper explores the semantic motivation of postmodal auxiliaries in complement constructions conveying mirativity in French and Finnish. French pouvoir ‘can’ and Finnish pitää ‘should’ both occur as postmodal markers in complements of epistemic and axiological items. These constructions refer to events that deviate from what is discursively projected as expected. As a modal verb of possibility, pouvoir profiles the meaning ‘p and not ¬p’, which is based on an opposition, while pitää, originally a necessity verb, gives prominence to the paradigmatic meaning ’p instead of q1, q2 …’. While the two verbs function in a similar manner as indexes of an interclausal semantic link in mirative constructions, the meaning of unexpectedness is not construed in the same way, and the critical contexts in the evolution of postmodal complement patterns with pouvoir and pitää are of a different type.