The purpose of the study is a comparative legal analysis of approaches to principles and rules in R. Alexy’s dual theory of law. The methodological basis of the study are the following fundamental methods of scientific knowledge: general methods (analysis, synthesis, induction, deduction, analogy), as well as special methods (comparative-legal and formal-legal). The application of these methods allowed to subject R. Alexy’s theory of law to an in-depth comparative legal study and to reveal the dichotomy of the principles and rules operating in it. The result of the study was the author’s conclusion that weighing formal and material principles is not only possible, but also a necessary process. In addition, it should be mentioned that the dictate of optimization always requires the implementation of a weighing procedure, and that principles in theory are always implemented indirectly through rules. The principles themselves are the subject of optimization, and the dictate of optimization is the rule. Thus, principles are the basis of rules, and rules are the product of principles. The novelty of the study lies in the author’s approach to the analysis of the dichotomy of principles and rules in the dual theory of law of R. Alexy, as well as the application of mathematical apparatus to substantiate the findings.