In this article, I want to consider the commitment to ontological naturalism and non-cognitivism on the part of the Scandinavian realists and its implications for their view of the nature of law. I argue (i) that the Scandinavians differ from legal positivists in that they reject the idea that there are legal relations, that is, legal entities and properties, and to varying degrees defend the view that law is a matter of human behavior rather than legal norms, and (ii) that although they cannot and do not accept either the idea that there is a ‘world of the ought’ in Kelsen’s sense, or the idea that law has a dual nature in the sense that it involves a non-naturalist account of legal correctness, they can accept a dual-nature theory of law of the type proposed by Robert Alexy, that is, a dual-nature theory that involves a constructivist conception of legal truth or validity. I also argue, more specifically, (iii) that the objection to non-naturalist theories raised by the Scandinavians – that there is and can be no connection between the higher realm of norms and values (the ‘world of the ought’) and the world of time and space – is convincing, (iv) and that Kelsen’s introduction of a so-called modally indifferent substrate does nothing to undermine this objection. Moreover, I argue (v) that although Alf Ross’s objection to dual-nature theories – that they give rise to certain antinomies – applies not only to non-naturalist dual-nature theories, but also to Alexy’s constructivist dual-nature theory, the objection fails since no antinomies arise either in Alexy’s theory or in other dual-nature theories. In addition, I argue (vi) that the Scandinavians can account for the existence of legal relations that do not presuppose the existence of morally binding legal norms by embracing conventionalism about the existence of the sources of law, while pointing out that in doing so they would also be abandoning their legal realism for legal positivism. Finally, I argue (vii) that the claims by Lundstedt, and to a lesser extent by Olivecrona and Ross, about the proper methods and study object of legal scholars are exaggerated, because (as I just hinted) we can easily conceive of legal relations along conventionalist lines.