Abstract: The universal conception of necessity says that necessary truth is truth in all possible worlds. This idea is well studied in the context of classical possible worlds models, and there its logic is S5. The universal conception of necessity is less well studied in non-classical models, and depending on the logic may differ from that of S5. We will present some preliminary results on universal necessity in frames for intuitionistic logic and for relevant logics. We will then present some general results about universal necessity using algebraic methods. This is joint work with Rohan French.