This paper discusses the syntactic variation of modal predicates between structures with a nominative primary argument and those with an oblique primary argument. In the literature, this variation is related to a change from deontic to epistemic meanings, whereby epistemicity seems to be more commonly expressed by highly grammaticalized impersonal constructions. After having shown the weakness of this relationship, I suggest a new explanation for the variation of modal predicates on the basis of diverse ancient Indo‐European languages, such as Vedic, Ancient Greek and Latin, as well as of some of their modern descendants, especially Hindi, Modern Greek, and standard and colloquial Italian. I argue that modal predicates with an oblique primary argument are favoured for functions of necessity, while modal predicates with a nominative primary argument preferably express functions of possibility. This reflects the different meanings of the lexical sources of these predicates, that is, capacity or power for predicates of possibility, and lack or obligation for predicates of necessity, which also imply different degrees of agentivity and control.