This investigation is a contribution to understudied areas of Australian Aboriginal linguistics and linguistic typology: the negation of existential and possessive clauses. It focuses on two structurally unusual negative verbless constructions in Nyulnyul (Nyulnyulan, Kimberley, Western Australia): a negative possessive indicating that a possessor lacks possessions of a specified type; and a negative existential indicating the absence of entities of the specified type at a particular location. Formal and semantic evidence is presented showing that these represent two distinct constructions. It is suggested that the negative existential emerged via reanalysis of a subtype of the negative possessive construction through a diachronic process that was not motivated by metaphorical or metonymic transfer, but by purely formal and pragmatic reinterpretations.