Binominal NPs (BNP) (e.g., a hell of a problem) are of empirical and theoretical interest due to their complex syntactic and semantic properties. In this paper, we review some basic properties of the BNP construction, focusing on its headedness, semantic relations, and the role of the preposition of. We argue that these properties suggest an account in the spirit of construction grammar. In particular, we show that English BNP is a nominal juxtaposition construction whose special syntactic constraints are linked to semantic relations like a subject-predicate relation.