  We present a class of solutions in Einstein-Yang-Mills-systems with arbitrary
gauge groups and space-time dimensions, which are symmetric under the action of
the group of spatial rotations. Our approach is based on the dimensional
reduction method for gauge and gravitational fields and relates symmetric
EYM-solutions to certain solutions of two-dimensional
Einstein-Yang-Mills-Higgs-dilaton theory. Application of this method to
four-dimensional spherically symmetric (pseudo)riemannian space-time yields, in
particular, new solutions describing both a magnetic and an electric charge in
the center of a black hole. Moreover, we give an example of a solution with
nonabelian gauge group in six-dimensional space-time. We also comment on the
stability of the obtained solutions.
