In this article, I discuss the emergence of verbal periphrasis with eἰμί “I am” and ἔχω “I have” and a perfect, present or aorist participle in Archaic and Classical Greek. Adopting a so-called ‘ecological’ perspective, I argue for the importance of looking at the interrelationship between the periphrastic constructions in terms of their origins and development, drawing particular attention to the mechanism of ‘intraference’. I relate their semantic development to the notion of ‘transitivity’ (in a generalized, gradual sense) and show that ἔχω with aorist participle, eἰμί with perfect participle and eἰμί with present participle became used in increasingly more transitive contexts, a process which I propose to call ‘transitivization’. Somewhat tentatively, I suggest that this notion can also be used to describe the semantic development of periphrasis in general, first having occurred in the domain of perfect aspect, afterwards in that of imperfective aspect and only in a final stage in that of perfective aspect.