  We prove local existence and uniqueness of static spherically symmetric
solutions of the Einstein-Yang-Mills equations for an arbitrary compact
semisimple gauge group in the so-called regular case. By this we mean the
equations obtained when the rotation group acts on the principal bundle on
which the Yang-Mills connection takes its values in a particularly simple way
(the only one ever considered in the literature). The boundary value problem
that results for possible asymptotically flat soliton or black hole solutions
is very singular and just establishing that local power series solutions exist
at the center and asymptotic solutions at infinity amounts to a nontrivial
algebraic problem. We discuss the possible field equations obtained for
different group actions and solve the algebraic problem on how the local
solutions depend on initial data at the center and at infinity.
