The division of powers between Federal and State governments and its interpretation by constitutional courts are fundamental elements of a federal system and of Federal-State power relations. The exclusivity or concurrence of powers, supremacy, and the problem of implied powers are some of the issues that appear in the constitutional law of most federations, and indeed stem from the very logic of a federal structure. However, the theoretical literature on federalism has not produced any satisfactory explanation of this logic. This article shows how W.N. Hohfeld’s fundamental legal conceptions may be used to analyse Federal-State relations, and how they are directly applicable in the context of ‘intergovernmental immunities’. The article then elaborates a theory of ‘tertiary’ legal relations, i.e., those arising when the two levels of government act in their regulatory capacity; these relations flow from the triangular nature of the relationship between the two governments and those subject to legislation. The correlations identified between Federal and State powers provide a conceptual framework within which different constitutional questions may be analysed. Adopting Hohfeld’s method of highlighting legal concepts in extracts from judicial decisions, the article uses examples from the case-law of several different federal countries.