Fr��licher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C^\infty(M,G) or \Diff(M), but also projective limits of Lie groups are in a natural way objects of that category, and group operations are morphisms in the category. We call groups with this property Fr��licher groups. One can define tangent spaces to Fr��licher spaces, and in the present article we prove that, under a certain additional assumption, the tangent space at the identity of a Fr��licher group can be equipped with a Lie bracket. We discuss an example which satisfies the additional assumption.

18 pages