In the paper I develop an LFG analysis of two noun phrase types in Hungarian that can be referred to as elliptical. In one of them, in Type (A), the understood noun head is entirely missing from the construction, and formally the head function is performed by the head of the final modifying constituent in the phrase. The major task here is to capture, in a lexicalist framework, the formal head properties of an adjective or a numeral. I employ an exocentric structure and introduce a pro noun head into f-structure by an appropriate functional annotation. In Type (B), which is always a (special) possessive construction, the noun head is represented by a pro-like morpheme attaching to the head of the possessor constituent. The fundamental challenge with respect to this construction type is that the morpheme appears to be phrasal in nature, and it can be recursively attached to the head, optionally in combination with the morpheme marking the plurality of the possessed noun. I assume that the morpheme in question is an argument taking predicate, and I capture scope relations and the possibility of recursion by means of a hierarchical sublexical representation.