A distinctive feature of Finnish morphology is the possessive suffixes, which are found not only on possessed nouns, but also on adjectives, postpositions, and untensed verbs. Traditional grammars have taken the view that these suffixes arise through a rule of agreement with a genitive specifier, which may be subject to subsequent deletion rules. This paper shows that they are not agreement markers, but rather clitic allomorphs of the reflexive pronoun. X-bar theory is used to formulate rules governing their distribution.*