ABSTRACT: The analysis of Lie groups depends to a large extent on their maximal tori. For a compact connected topological group G, the subgroups analogous to the maximal tori are the maximal connected Abelian subgroups. As in Hofmann and Morris [7] we call them maximal protori. We sharpen some results of [7] by showing that each maximal protorus is in a natural way the projective limit of maximal tori Tα in the corresponding Gα, where G= projGα. This sharpened characterization together with some methods of Moskowitz [4], [10] will be used to show that a number of well‐known theorems concerning Lie groups extend in a natural way to all compact connected groups.