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This paper investigates the semantic composition of Russian possessive constructions. It is argued that in sentences of the kind u X est' Y, the Y-expression is used to refer to a type. Accordingly, the nominal sobaka in a sentence like U Igorja est' sobaka denotes the type ‘dog’. The fact that the sentence (utterance) is nevertheless about a particular dog, i.e. about some token of the type, is explained by the semantic impact of the existence predicate est'. It is demonstrated how the proposed analysis can account for the linguistic data known about Russian possessive constructions, and how it can be implemented in terms of DRT.