<p>Inspired by the well-known Stone’s duality and Priestley’s duality for the class of distributive lattices, Celani and Calomino built a Stone-style duality for the class of distributive nearlattices with greatest element and González presented a Priestley-style duality for the variety of DN-algebras. As we know, the category of distributive nearlattices with greatest element and the category of DN-algebras with greatest element are equivalent, then it is natural to develop the Priestley-style duality for the class of distributive nearlattices with greatest element and consider the relationship between the categories of Stone-like spaces and Priestley-like spaces both for distributive nearlattices with greatest element. In this paper, we shall modify the Stone-style duality for the class of distributive nearlattices with greatest element and present a Priestley-style duality for the class of distributive nearlattices with greatest element. Furthermore, it will be shown that the category of Priestley-like spaces with certain binary relations and the category of Stone-like spaces with certain binary relations are isomorphic.</p>