Abstract
After a brief discussion of some surprising recent discoveries (colored black holes, etc.) for the Einstein-Yang-Mills (EYM) system and for related systems with nonlinear matter models, a report on work in progress is given, in which the authors started a more systematic study of the coupled EYM equations for arbitrary gauge groups. In a first step a group theoretical analysis of spherically symmetric EYM fields is given. This will lead to a concise description of a large class of principal bundles for which the spherically symmetric solutions of the EYM equations have to be static (generalized Birkhoff theorem) and the metric must be of the Reissner-Nordstrom type. Some results on 'no hair theorems', established recently with the help of scaling arguments, are also briefly discussed.