We define when a ternary term m of an algebraic language \ is called a distributive nearlattice term -term) of a sentential logic \. Distributive nearlattices are ternary algebras generalising Tarski algebras and distributive lattices. We characterise the selfextensional logics with a \-term through the interpretation of the DN-term in the algebras of the algebraic counterpart of the logics. We prove that the canonical class of algebras associated with a selfextensional logic with a \-term is a variety, and we obtain (...) that the logic is in fact fully selfextensional. (shrink)