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Legal positivists often claim that law is a limited normative domain. Understanding the limits of law requires an answer to two related problems. On the one hand, the problem of unregulated cases and, on the other hand, the problem of the alien norms. The first problem refers to the distinction between legal gaps and unregulated cases. Many legal philosophers claim that the identification of legal gaps presupposes an evaluative judgment. Thus, contrary to legal positivism, the determination of the content and limits of law (i.e., the domain of regulated cases) does not only depend on the cognition of certain social facts, but it actually also requires an evaluation of such facts. The second problem refers to the fact that judges often recognize as legally binding norms that are not issued by competent authorities of their systems. Therefore, a positivistic theory would not provide a satisfactory account of law if it failed to explain the legal force of this kind of norms. In this paper I analyze some solutions to such problems that can be found in three well-known positivistic theories (Kelsen, Raz and Bulygin). I show that none of them offers a sound answer to the problem of the unregulated cases and the alien norms. [ABSTRACT FROM AUTHOR]