In this paper, which discusses data from Gargano Apulian Italo‐Romance, I propose that prepositional and non‐prepositional genitives are fundamentally two different types of phrases, and that the interpretation of a non‐prepositional noun as the possessor is not due to a silent preposition or head‐modifier inversion, but rather to an agreement mechanism taking place between the modifier and its head. We propose that, just as a genitive can agree with its head for gender and number features so it can for definiteness, and that agreement for definiteness yields a genitival interpretation of the non‐prepositional noun. I.e., definiteness can externalize the syntactic relation between head and modifier. We also propose that in this Apulian variety, non‐prepositional genitives are syntactic phases (Chomsky 2001), and that the same holds for non‐prepositional ‘qualitative’ predicative phrases in the same language. This would explain the impossibility of accessing the phrase through syntactic operations such as extraction.