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This paper tries to resolve a conflict in the literature on the connection between ‘rich ’ agreement and argument-drop. Jelinek (1984) claims that inflectional affixes in polysynthetic languages are theta-role bearing arguments; Baker (1991) argues that such affixes are agreement, bearing Case but no theta-role. Evidence from Yimas shows that both of these views can be correct, within a single language. Explanation of what kind of inflection is used where also provides us with an account of the unusual split ergative agreement system of Yimas, and suggests a novel explanation for the ban on subject incorporation, and some exceptions to the ban. 1. Two types of inflection My main aim in this paper is to demonstrate that inflectional affixes can be very different kinds of syntactic objects, even within a single language. I illustrate this point with evidence from Yimas, a Papuan language of New Guinea (Foley 1991). Understanding of the nature of the different inflectional affixes of Yimas provides an explanation for its remarkably elaborate agreement system, which follows a basic split-ergative scheme, but with a number of added complications. Anticipating my conclusions, the structure in (1c) shows what I assume the four principal case affixes on a Yimas verb to be. What I refer to as Nominative and Accusative affixes are pronominal arguments: these inflections, which are restricted to 1st and 2nd person arguments in Yimas, begin as specifiers and complements of the verb, and incorporate into the verb by Sstructure. On the other hand, what I refer to as Ergative and Absolutive inflection are genuine agreement- they are the spell-out of functional heads, above VP, which agree with an argument in their specifier. 1. a. Nominative & Accusative are Arguments, result of incorporation. b. Ergative & Absolutive are Agreement, product of Spec-Head relation