Debate on the relevance (or otherwise) of federalism to the development of the European Union is often characterised by mutual incomprehension on either side. Close inspection, however, reveals that the high temperature of argument may not be solely due to differing visions of the finalite politique. For the precise meaning of the federal concept in political science remains unsettled. This article looks back to the earliest origins of federalism, in order to establish a firm basis for suggesting improvements. The idea of divided sovereignty, ‘invented’ in America and now thought to lie at the heart of the federal concept, is identified to be a false construction. On these grounds, it is proposed that the definition of federalism be clarified today as not ‘a division of sovereignty between two levels of government’, but instead ‘a division of the powers flowing from sovereignty between two levels of government of equal status’.