This paper suggests an analysis of Modern Hebrew noun phrases in the framework of HPSG. It focuses on the peculiar properties of the definite article, including the requirement for definiteness agreement among various elements in the noun phrase, definiteness inheritance in construct-state nominals, the fact that the article does not combine with constructs and the similarities between construct-state nouns and adjectives. Central to our analysis is the assumption that the Hebrew definite article is an affix, rather than a clitic or a stand-alone word. Several arguments, from all levels of linguistic representation, are provided to justify this claim. Adopting the lexical hypothesis, we conclude that the article combines with nominals in the lexicon, and is no longer available for syntactic processes. This leads to an analysis of noun phrases as NPs, rather than as DPs; we show that such a view is compatible with accepted criteria for headedness. We provide an HPSG analysis that covers the above mentioned phenomena, correctly predicting the location of the definite article in constructs, accounting for definiteness agreement and definiteness inheritance constraints, and yielding similar structures for the two major ways of expressing genitive relations in Hebrew.