A term category of possessivity belongs for sure to the group of the universal language categories. It probably exists in all the languages and it is concerned with the relations of ownership, which means the fact of beeing an owner or a property. This relationship may be expressed by different expression measures. The most important would be a possessive adjective. However, it seems its use in different languages is not submitted to the same logic, which proves that not only linguistic but also grammatical units in many languages serve to express different concepts. This article deals with the criterions of usage of the possessive adjective in French language. The analysed examples show a polisemy of this element of sentence, as an expression of the real ownership or different ways of connections.